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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 4, 2, 3, 2, 3, 2, 4, 12, 6, 2, 2], 'aut_gens': [[1967901282, 20650453574, 1137300, 13412085385, 1134054, 2587950, 19770831414, 2951738, 647, 526], [131728482, 19771557374, 1137300, 6266978185, 1862886, 1134054, 20649729846, 1500825, 647, 526], [38366295721, 38480887140, 2586614, 6398341006, 1134054, 2587950, 39798138294, 2953385, 265, 647], [38366295060, 20649002535, 2585677, 6398341127, 2587950, 1134054, 39799592190, 3314314, 265, 526], [1967901775, 20650453695, 1137421, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [1968624140, 20649004260, 1860014, 13412085385, 1862886, 1134054, 19771560246, 2950397, 647, 526], [1967901661, 20650453801, 1137535, 13412085385, 1134054, 2587950, 19770831414, 3312825, 647, 526], [1968624489, 20650453338, 1859900, 13412085646, 2587950, 1862886, 19772285310, 2227076, 265, 647], [1969350618, 20649004260, 2586614, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [1967900162, 20649727747, 1861038, 13414673070, 526, 265, 19770469006, 1499368, 1862886, 1134054], [19281634741, 20649003008, 1861164, 33657846407, 1134054, 1862886, 19770831414, 1499237, 265, 526], [38009907198, 20650452637, 1860661, 13412085646, 1862886, 2587950, 19771560246, 2950397, 647, 265], [1967899815, 20649728124, 1136048, 13412085767, 1134054, 1862886, 19770831414, 2953385, 265, 526], [1968624140, 20648639820, 1860014, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526]], 'aut_group': '41472.kr', 'aut_hash': 5131433462079402963, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 18, 'aut_perms': [411983379178183, 3749202155315406, 3545741967387042, 963509458501813, 2081150988625839, 3378972814955679, 4843649503987599, 2752595349187335, 381766239340959, 4772987184755438, 304015548606301, 1956044373264270, 3314718500685517], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 2, 1], [2, 3, 3, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 9, 6, 1], [2, 12, 1, 1], [2, 18, 2, 1], [2, 27, 3, 1], [2, 36, 2, 1], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 32, 1, 1], [3, 64, 2, 1], [3, 128, 1, 1], [4, 12, 3, 1], [4, 36, 6, 1], [4, 108, 3, 1], [6, 6, 2, 1], [6, 6, 6, 1], [6, 12, 2, 1], [6, 12, 3, 1], [6, 18, 6, 1], [6, 24, 1, 1], [6, 24, 2, 1], [6, 36, 2, 1], [6, 48, 1, 1], [6, 72, 2, 1], [6, 96, 2, 1], [6, 192, 2, 1], [6, 288, 1, 1], [12, 24, 6, 1], [12, 48, 3, 1], [12, 72, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4^2:(C_6^2:D_4)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '41472.kr', 'autcentquo_hash': 5131433462079402963, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'A_4^2:(C_6^2:D_4)', 'cc_stats': [[1, 1, 1], [2, 3, 5], [2, 6, 1], [2, 9, 7], [2, 12, 1], [2, 18, 2], [2, 27, 3], [2, 36, 2], [2, 54, 1], [2, 108, 1], [3, 2, 2], [3, 4, 1], [3, 32, 1], [3, 64, 2], [3, 128, 1], [4, 12, 3], [4, 36, 6], [4, 108, 3], [6, 6, 8], [6, 12, 5], [6, 18, 6], [6, 24, 3], [6, 36, 2], [6, 48, 1], [6, 72, 2], [6, 96, 2], [6, 192, 2], [6, 288, 1], [12, 24, 6], [12, 48, 3], [12, 72, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '3456.oc', 'commutator_count': 1, 'commutator_label': '432.771', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 367, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['6.1', 2], ['96.227', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 5], [2, 6, 1, 1], [2, 9, 1, 7], [2, 12, 1, 1], [2, 18, 1, 2], [2, 27, 1, 3], [2, 36, 1, 2], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 32, 1, 1], [3, 64, 1, 2], [3, 128, 1, 1], [4, 12, 1, 3], [4, 36, 1, 6], [4, 108, 1, 3], [6, 6, 1, 8], [6, 12, 1, 5], [6, 18, 1, 6], [6, 24, 1, 3], [6, 36, 1, 2], [6, 48, 1, 1], [6, 72, 1, 2], [6, 96, 1, 2], [6, 192, 1, 2], [6, 288, 1, 1], [12, 24, 1, 6], [12, 48, 1, 3], [12, 72, 1, 6]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 188160, 'exponent': 12, 'exponents_of_order': [7, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3456.oc', 'hash': 1942231094641922994, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 3, 3, 2, 2, 2, 6, 4, 2, 2], 'inner_gens': [[1967901282, 38481610203, 1137535, 13412085767, 1862886, 1134054, 39798867126, 1499368, 526, 265], [38008819285, 20650453574, 1740, 13412085767, 1862886, 1134054, 19771560246, 3315793, 526, 265], [1967901661, 20649726974, 1137300, 13412085767, 1862886, 1134054, 19771560246, 2224553, 526, 265], [1967901661, 20650453801, 1137535, 13412085385, 1134054, 2587950, 39798138294, 3312825, 647, 526], [1968624140, 20648639820, 1860014, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1969350618, 20649004260, 2586614, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [38365568780, 20648639820, 1860014, 6398340745, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1969350294, 20649003008, 1135922, 13413948006, 647, 526, 19770469127, 2951738, 1134054, 2587950], [1967901540, 20650453338, 1137042, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1967901775, 20650453695, 1137421, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526]], 'inner_hash': 1942231094641922994, 'inner_nilpotent': False, 'inner_order': 3456, 'inner_split': True, 'inner_tex': 'D_6^2:S_4', 'inner_used': [1, 2, 3, 4, 7, 8], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 12], [3, 24], [4, 6], [6, 28], [8, 1], [12, 10], [24, 1]], 'label': '3456.oc', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'D6^2:S4', 'ngens': 10, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 90, 'number_divisions': 90, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 1371, 'number_subgroup_classes': 6076, 'number_subgroups': 108168, 'old_label': None, 'order': 3456, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 447], [3, 296], [4, 576], [6, 1416], [12, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[1968624489, 20650453574, 2586735, 13413219174, 265, 526, 19770468745, 3313306, 1862886, 2587950], [491060815, 19770470106, 1137042, 32736131207, 2587950, 1862886, 20650454910, 2226401, 526, 265]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 24], [4, 6], [6, 28], [8, 1], [12, 10], [24, 1]], 'representations': {'PC': {'code': '622303824504332067194411511885159116499883416332385257510299324141683289875953190773847234731181092711588', 'gens': [1, 2, 4, 6, 7, 9, 10], 'pres': [10, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 17640, 17481, 51, 39122, 121443, 61693, 30743, 113, 1214, 185765, 28095, 7585, 133566, 40336, 17666, 756, 206, 23057, 697, 42128, 58338, 9748, 129609, 23419, 54929]}, 'Perm': {'d': 14, 'gens': [1967901282, 20650453574, 1137300, 13412085385, 1134054, 2587950, 19770831414, 2951738, 647, 526]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6^2:S_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 160435835
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 367, 'group_order': 3456, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 160435846
{'aut_label': '2A', 'centralizer': '3.a1', 'counter': 2, 'group_counter': 367, 'group_order': 3456, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 33657845760, 'size': 3}
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id: 160435857
{'aut_label': '2A', 'centralizer': '3.a1', 'counter': 3, 'group_counter': 367, 'group_order': 3456, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 14860702080, 'size': 3}
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id: 160435868
{'aut_label': '2C', 'centralizer': '3.b1', 'counter': 4, 'group_counter': 367, 'group_order': 3456, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1134289, 'size': 3}
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id: 160435879
{'aut_label': '2C', 'centralizer': '3.b1', 'counter': 5, 'group_counter': 367, 'group_order': 3456, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1863138, 'size': 3}
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id: 160435890
{'aut_label': '2C', 'centralizer': '3.b1', 'counter': 6, 'group_counter': 367, 'group_order': 3456, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 2588323, 'size': 3}
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id: 160435901
{'aut_label': '2F', 'centralizer': '6.b1', 'counter': 7, 'group_counter': 367, 'group_order': 3456, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 265, 'size': 6}
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id: 160435912
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 8, 'group_counter': 367, 'group_order': 3456, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 33658208929, 'size': 9}
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id: 160435923
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 9, 'group_counter': 367, 'group_order': 3456, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 33658209212, 'size': 9}
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id: 160435836
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 10, 'group_counter': 367, 'group_order': 3456, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 33658209333, 'size': 9}
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id: 160435837
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 11, 'group_counter': 367, 'group_order': 3456, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 14861065249, 'size': 9}
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id: 160435838
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 12, 'group_counter': 367, 'group_order': 3456, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 14861065532, 'size': 9}
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id: 160435839
{'aut_label': '2G', 'centralizer': '9.b1', 'counter': 13, 'group_counter': 367, 'group_order': 3456, 'label': '2L', 'order': 2, 'powers': [1, 13], 'representative': 14861065653, 'size': 9}
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id: 160435840
{'aut_label': '2M', 'centralizer': '9.a1', 'counter': 14, 'group_counter': 367, 'group_order': 3456, 'label': '2M', 'order': 2, 'powers': [1, 14], 'representative': 1967535360, 'size': 9}
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id: 160435841
{'aut_label': '2N', 'centralizer': '12.w1', 'counter': 15, 'group_counter': 367, 'group_order': 3456, 'label': '2N', 'order': 2, 'powers': [1, 15], 'representative': 1499116, 'size': 12}
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id: 160435842
{'aut_label': '2O', 'centralizer': '18.o1', 'counter': 16, 'group_counter': 367, 'group_order': 3456, 'label': '2O', 'order': 2, 'powers': [1, 16], 'representative': 33657846025, 'size': 18}
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id: 160435843
{'aut_label': '2O', 'centralizer': '18.o1', 'counter': 17, 'group_counter': 367, 'group_order': 3456, 'label': '2P', 'order': 2, 'powers': [1, 17], 'representative': 14860702345, 'size': 18}
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id: 160435844
{'aut_label': '2Q', 'centralizer': '27.a1', 'counter': 18, 'group_counter': 367, 'group_order': 3456, 'label': '2Q', 'order': 2, 'powers': [1, 18], 'representative': 131725729, 'size': 27}
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id: 160435845
{'aut_label': '2Q', 'centralizer': '27.a1', 'counter': 19, 'group_counter': 367, 'group_order': 3456, 'label': '2R', 'order': 2, 'powers': [1, 19], 'representative': 131726012, 'size': 27}
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id: 160435847
{'aut_label': '2Q', 'centralizer': '27.a1', 'counter': 20, 'group_counter': 367, 'group_order': 3456, 'label': '2S', 'order': 2, 'powers': [1, 20], 'representative': 131726133, 'size': 27}
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id: 160435848
{'aut_label': '2T', 'centralizer': '36.bf1', 'counter': 21, 'group_counter': 367, 'group_order': 3456, 'label': '2T', 'order': 2, 'powers': [1, 21], 'representative': 6400521224, 'size': 36}
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id: 160435849
{'aut_label': '2T', 'centralizer': '36.bf1', 'counter': 22, 'group_counter': 367, 'group_order': 3456, 'label': '2U', 'order': 2, 'powers': [1, 22], 'representative': 6268477036, 'size': 36}
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id: 160435850
{'aut_label': '2V', 'centralizer': '54.g1', 'counter': 23, 'group_counter': 367, 'group_order': 3456, 'label': '2V', 'order': 2, 'powers': [1, 23], 'representative': 131362825, 'size': 54}
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id: 160435851
{'aut_label': '2W', 'centralizer': '108.p1', 'counter': 24, 'group_counter': 367, 'group_order': 3456, 'label': '2W', 'order': 2, 'powers': [1, 24], 'representative': 38011362479, 'size': 108}
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id: 160435852
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 25, 'group_counter': 367, 'group_order': 3456, 'label': '3A', 'order': 3, 'powers': [25, 1], 'representative': 20648638080, 'size': 2}
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id: 160435853
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 26, 'group_counter': 367, 'group_order': 3456, 'label': '3B', 'order': 3, 'powers': [26, 1], 'representative': 19770468480, 'size': 2}
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id: 160435854
{'aut_label': '3C', 'centralizer': '4.c1', 'counter': 27, 'group_counter': 367, 'group_order': 3456, 'label': '3C', 'order': 3, 'powers': [27, 1], 'representative': 1919998080, 'size': 4}
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id: 160435855
{'aut_label': '3D', 'centralizer': '32.c1', 'counter': 28, 'group_counter': 367, 'group_order': 3456, 'label': '3D', 'order': 3, 'powers': [28, 1], 'representative': 3494, 'size': 32}
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id: 160435856
{'aut_label': '3E', 'centralizer': '64.a1', 'counter': 29, 'group_counter': 367, 'group_order': 3456, 'label': '3E', 'order': 3, 'powers': [29, 1], 'representative': 20649727323, 'size': 64}
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id: 160435858
{'aut_label': '3E', 'centralizer': '64.a1', 'counter': 30, 'group_counter': 367, 'group_order': 3456, 'label': '3F', 'order': 3, 'powers': [30, 1], 'representative': 39797778854, 'size': 64}
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id: 160435859
{'aut_label': '3G', 'centralizer': '128.a1', 'counter': 31, 'group_counter': 367, 'group_order': 3456, 'label': '3G', 'order': 3, 'powers': [31, 1], 'representative': 602745420, 'size': 128}
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id: 160435860
{'aut_label': '4A', 'centralizer': '12.x1', 'counter': 32, 'group_counter': 367, 'group_order': 3456, 'label': '4A', 'order': 4, 'powers': [4, 32], 'representative': 2224180, 'size': 12}
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id: 160435861
{'aut_label': '4A', 'centralizer': '12.x1', 'counter': 33, 'group_counter': 367, 'group_order': 3456, 'label': '4B', 'order': 4, 'powers': [5, 33], 'representative': 2952746, 'size': 12}
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id: 160435862
{'aut_label': '4A', 'centralizer': '12.x1', 'counter': 34, 'group_counter': 367, 'group_order': 3456, 'label': '4C', 'order': 4, 'powers': [6, 34], 'representative': 3315672, 'size': 12}
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id: 160435863
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 35, 'group_counter': 367, 'group_order': 3456, 'label': '4D', 'order': 4, 'powers': [6, 35], 'representative': 32736858929, 'size': 36}
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id: 160435864
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 36, 'group_counter': 367, 'group_order': 3456, 'label': '4E', 'order': 4, 'powers': [4, 36], 'representative': 32737583620, 'size': 36}
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id: 160435865
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 37, 'group_counter': 367, 'group_order': 3456, 'label': '4F', 'order': 4, 'powers': [5, 37], 'representative': 13414309673, 'size': 36}
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id: 160435866
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 38, 'group_counter': 367, 'group_order': 3456, 'label': '4G', 'order': 4, 'powers': [6, 38], 'representative': 13414309552, 'size': 36}
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id: 160435867
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 39, 'group_counter': 367, 'group_order': 3456, 'label': '4H', 'order': 4, 'powers': [5, 39], 'representative': 32737586516, 'size': 36}
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id: 160435869
{'aut_label': '4D', 'centralizer': '36.bg1', 'counter': 40, 'group_counter': 367, 'group_order': 3456, 'label': '4I', 'order': 4, 'powers': [4, 40], 'representative': 33660390694, 'size': 36}
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id: 160435870
{'aut_label': '4J', 'centralizer': '108.q1', 'counter': 41, 'group_counter': 367, 'group_order': 3456, 'label': '4J', 'order': 4, 'powers': [6, 41], 'representative': 1970079912, 'size': 108}
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id: 160435871
{'aut_label': '4J', 'centralizer': '108.q1', 'counter': 42, 'group_counter': 367, 'group_order': 3456, 'label': '4K', 'order': 4, 'powers': [4, 42], 'representative': 20680178134, 'size': 108}
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id: 160435872
{'aut_label': '4J', 'centralizer': '108.q1', 'counter': 43, 'group_counter': 367, 'group_order': 3456, 'label': '4L', 'order': 4, 'powers': [5, 43], 'representative': 133905754, 'size': 108}
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id: 160435873
{'aut_label': '6A', 'centralizer': '6.c1', 'counter': 44, 'group_counter': 367, 'group_order': 3456, 'label': '6A', 'order': 6, 'powers': [25, 2], 'representative': 7192684800, 'size': 6}
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id: 160435874
{'aut_label': '6A', 'centralizer': '6.c1', 'counter': 45, 'group_counter': 367, 'group_order': 3456, 'label': '6B', 'order': 6, 'powers': [26, 3], 'representative': 7348682880, 'size': 6}
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id: 160435875
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 46, 'group_counter': 367, 'group_order': 3456, 'label': '6C', 'order': 6, 'powers': [26, 4], 'representative': 39798138529, 'size': 6}
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id: 160435876
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 47, 'group_counter': 367, 'group_order': 3456, 'label': '6D', 'order': 6, 'powers': [26, 5], 'representative': 39798867378, 'size': 6}
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id: 160435877
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 48, 'group_counter': 367, 'group_order': 3456, 'label': '6E', 'order': 6, 'powers': [26, 6], 'representative': 39799592563, 'size': 6}
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id: 160435878
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 49, 'group_counter': 367, 'group_order': 3456, 'label': '6F', 'order': 6, 'powers': [25, 4], 'representative': 38480884129, 'size': 6}
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id: 160435880
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 50, 'group_counter': 367, 'group_order': 3456, 'label': '6G', 'order': 6, 'powers': [25, 5], 'representative': 38481612978, 'size': 6}
-
id: 160435881
{'aut_label': '6C', 'centralizer': '6.g1', 'counter': 51, 'group_counter': 367, 'group_order': 3456, 'label': '6H', 'order': 6, 'powers': [25, 6], 'representative': 38482338163, 'size': 6}
-
id: 160435882
{'aut_label': '6I', 'centralizer': '12.b1', 'counter': 52, 'group_counter': 367, 'group_order': 3456, 'label': '6I', 'order': 6, 'powers': [26, 7], 'representative': 19770468745, 'size': 12}
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id: 160435883
{'aut_label': '6I', 'centralizer': '12.b1', 'counter': 53, 'group_counter': 367, 'group_order': 3456, 'label': '6J', 'order': 6, 'powers': [25, 7], 'representative': 20648638345, 'size': 12}
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id: 160435884
{'aut_label': '6K', 'centralizer': '12.bw1', 'counter': 54, 'group_counter': 367, 'group_order': 3456, 'label': '6K', 'order': 6, 'powers': [27, 4], 'representative': 1920729169, 'size': 12}
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id: 160435885
{'aut_label': '6K', 'centralizer': '12.bw1', 'counter': 55, 'group_counter': 367, 'group_order': 3456, 'label': '6L', 'order': 6, 'powers': [27, 5], 'representative': 1921458018, 'size': 12}
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id: 160435886
{'aut_label': '6K', 'centralizer': '12.bw1', 'counter': 56, 'group_counter': 367, 'group_order': 3456, 'label': '6M', 'order': 6, 'powers': [27, 6], 'representative': 1922183203, 'size': 12}
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id: 160435887
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 57, 'group_counter': 367, 'group_order': 3456, 'label': '6N', 'order': 6, 'powers': [25, 8], 'representative': 7193451169, 'size': 18}
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id: 160435888
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 58, 'group_counter': 367, 'group_order': 3456, 'label': '6O', 'order': 6, 'powers': [25, 9], 'representative': 7193451452, 'size': 18}
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id: 160435889
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 59, 'group_counter': 367, 'group_order': 3456, 'label': '6P', 'order': 6, 'powers': [25, 10], 'representative': 7193451573, 'size': 18}
-
id: 160435891
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 60, 'group_counter': 367, 'group_order': 3456, 'label': '6Q', 'order': 6, 'powers': [26, 11], 'representative': 7349413969, 'size': 18}
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id: 160435892
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 61, 'group_counter': 367, 'group_order': 3456, 'label': '6R', 'order': 6, 'powers': [26, 12], 'representative': 7349414252, 'size': 18}
-
id: 160435893
{'aut_label': '6N', 'centralizer': '18.c1', 'counter': 62, 'group_counter': 367, 'group_order': 3456, 'label': '6S', 'order': 6, 'powers': [26, 13], 'representative': 7349414373, 'size': 18}
-
id: 160435894
{'aut_label': '6T', 'centralizer': '24.c1', 'counter': 63, 'group_counter': 367, 'group_order': 3456, 'label': '6T', 'order': 6, 'powers': [27, 7], 'representative': 602743945, 'size': 24}
-
id: 160435895
{'aut_label': '6U', 'centralizer': '24.t1', 'counter': 64, 'group_counter': 367, 'group_order': 3456, 'label': '6U', 'order': 6, 'powers': [26, 15], 'representative': 19771196476, 'size': 24}
-
id: 160435896
{'aut_label': '6U', 'centralizer': '24.t1', 'counter': 65, 'group_counter': 367, 'group_order': 3456, 'label': '6V', 'order': 6, 'powers': [25, 15], 'representative': 20649366076, 'size': 24}
-
id: 160435897
{'aut_label': '6W', 'centralizer': '36.n1', 'counter': 66, 'group_counter': 367, 'group_order': 3456, 'label': '6W', 'order': 6, 'powers': [25, 16], 'representative': 7192685065, 'size': 36}
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id: 160435898
{'aut_label': '6W', 'centralizer': '36.n1', 'counter': 67, 'group_counter': 367, 'group_order': 3456, 'label': '6X', 'order': 6, 'powers': [26, 17], 'representative': 7348683145, 'size': 36}
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id: 160435899
{'aut_label': '6Y', 'centralizer': '48.dc1', 'counter': 68, 'group_counter': 367, 'group_order': 3456, 'label': '6Y', 'order': 6, 'powers': [27, 15], 'representative': 603839596, 'size': 48}
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id: 160435900
{'aut_label': '6Z', 'centralizer': '72.q1', 'counter': 69, 'group_counter': 367, 'group_order': 3456, 'label': '6Z', 'order': 6, 'powers': [25, 21], 'representative': 14935423544, 'size': 72}
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id: 160435902
{'aut_label': '6Z', 'centralizer': '72.q1', 'counter': 70, 'group_counter': 367, 'group_order': 3456, 'label': '6AA', 'order': 6, 'powers': [26, 22], 'representative': 13584052156, 'size': 72}
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id: 160435903
{'aut_label': '6AB', 'centralizer': '96.n1', 'counter': 71, 'group_counter': 367, 'group_order': 3456, 'label': '6AB', 'order': 6, 'powers': [28, 3], 'representative': 14860703820, 'size': 96}
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id: 160435904
{'aut_label': '6AB', 'centralizer': '96.n1', 'counter': 72, 'group_counter': 367, 'group_order': 3456, 'label': '6AC', 'order': 6, 'powers': [28, 2], 'representative': 13412088381, 'size': 96}
-
id: 160435905
{'aut_label': '6AD', 'centralizer': '192.c1', 'counter': 73, 'group_counter': 367, 'group_order': 3456, 'label': '6AD', 'order': 6, 'powers': [29, 2], 'representative': 31299530661, 'size': 192}
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id: 160435906
{'aut_label': '6AD', 'centralizer': '192.c1', 'counter': 74, 'group_counter': 367, 'group_order': 3456, 'label': '6AE', 'order': 6, 'powers': [30, 3], 'representative': 31215342805, 'size': 192}
-
id: 160435907
{'aut_label': '6AF', 'centralizer': '288.k1', 'counter': 75, 'group_counter': 367, 'group_order': 3456, 'label': '6AF', 'order': 6, 'powers': [28, 14], 'representative': 1967537365, 'size': 288}
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id: 160435908
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 76, 'group_counter': 367, 'group_order': 3456, 'label': '12A', 'order': 12, 'powers': [46, 32], 'representative': 19771196597, 'size': 24}
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id: 160435909
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 77, 'group_counter': 367, 'group_order': 3456, 'label': '12B', 'order': 12, 'powers': [47, 33], 'representative': 19771196728, 'size': 24}
-
id: 160435910
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 78, 'group_counter': 367, 'group_order': 3456, 'label': '12C', 'order': 12, 'powers': [48, 34], 'representative': 19771196849, 'size': 24}
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id: 160435911
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 79, 'group_counter': 367, 'group_order': 3456, 'label': '12D', 'order': 12, 'powers': [49, 32], 'representative': 20649366197, 'size': 24}
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id: 160435913
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 80, 'group_counter': 367, 'group_order': 3456, 'label': '12E', 'order': 12, 'powers': [50, 33], 'representative': 20649366328, 'size': 24}
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id: 160435914
{'aut_label': '12A', 'centralizer': '24.z1', 'counter': 81, 'group_counter': 367, 'group_order': 3456, 'label': '12F', 'order': 12, 'powers': [51, 34], 'representative': 20649366449, 'size': 24}
-
id: 160435915
{'aut_label': '12G', 'centralizer': '48.dr1', 'counter': 82, 'group_counter': 367, 'group_order': 3456, 'label': '12G', 'order': 12, 'powers': [54, 32], 'representative': 603839717, 'size': 48}
-
id: 160435916
{'aut_label': '12G', 'centralizer': '48.dr1', 'counter': 83, 'group_counter': 367, 'group_order': 3456, 'label': '12H', 'order': 12, 'powers': [55, 33], 'representative': 603839848, 'size': 48}
-
id: 160435917
{'aut_label': '12G', 'centralizer': '48.dr1', 'counter': 84, 'group_counter': 367, 'group_order': 3456, 'label': '12I', 'order': 12, 'powers': [56, 34], 'representative': 603839969, 'size': 48}
-
id: 160435918
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 85, 'group_counter': 367, 'group_order': 3456, 'label': '12J', 'order': 12, 'powers': [48, 35], 'representative': 12504566952, 'size': 72}
-
id: 160435919
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 86, 'group_counter': 367, 'group_order': 3456, 'label': '12K', 'order': 12, 'powers': [46, 36], 'representative': 12502750517, 'size': 72}
-
id: 160435920
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 87, 'group_counter': 367, 'group_order': 3456, 'label': '12L', 'order': 12, 'powers': [50, 37], 'representative': 8716019233, 'size': 72}
-
id: 160435921
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 88, 'group_counter': 367, 'group_order': 3456, 'label': '12M', 'order': 12, 'powers': [51, 38], 'representative': 31301347827, 'size': 72}
-
id: 160435922
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 89, 'group_counter': 367, 'group_order': 3456, 'label': '12N', 'order': 12, 'powers': [47, 39], 'representative': 8623489541, 'size': 72}
-
id: 160435924
{'aut_label': '12J', 'centralizer': '72.w1', 'counter': 90, 'group_counter': 367, 'group_order': 3456, 'label': '12O', 'order': 12, 'powers': [49, 40], 'representative': 12616621865, 'size': 72}
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gps_qchar • Show schema
Hide schema
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id: 15739140
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 15739151
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 15739162
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 15739173
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
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id: 15739184
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
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id: 15739195
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
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id: 15739206
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
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id: 15739217
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 15739228
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, -1, 2, 0, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, -1, 2, 0, -1, -1, 0, -1, 2, 0, 0, -1, 0, -1, 2, 2, -1, -1, 2, -1, -1, -1, 0, -1, -1, 0, -1, 0], 'schur_index': 1}
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id: 15739141
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, -1, -1, -1, -1, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, 2, -1, -1, 0, -1, -1, 0, 0, 2, -1, 0, 0, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1], 'schur_index': 1}
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id: 15739142
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739143
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 0, -2, -2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 0, 0, -2, -2, 0, 0, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739144
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 2, 2, 2, 2, -2, 0, -2, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, -2, -2, -2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, -1, 1, -1, -1, 0, 2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, -1, -2, 1, 1, 0, 1, -1, 0, 0, -2, 1, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, -1, 0, 0, -1, 0, -1], 'schur_index': 1}
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id: 15739145
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 2, 2, 2, 2, -2, 0, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, 2, 2, 2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 2, -1, 1, -1, -1, 0, 2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 0, 0, 0, -1, 2, -1, 1, 0, -1, 1, 0, 0, -2, 1, 0, 0, 2, -1, -1, 2, 2, -1, -1, -1, -1, 1, 0, 0, 1, 0, 1], 'schur_index': 1}
-
id: 15739146
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 0, -2, 2, -2, -2, -2, 0, 0, -2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 0, 0, -2, 2, 0, 0, 0, -1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739147
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 2, 2, 2, 2, 0, -2, 0, 0, 0, -2, -2, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, -2, 2, 0, 2, 0, 0, 2, 0, 0, 0, -1, 2, 0, 2, 2, 1, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 1, 1, 1, -1, 1, -2, 0, 1, 1, 0, -1, -2, 0, 0, 1, 0, 1, -2, -2, 1, 1, -2, 1, 1, 1, 0, -1, -1, 0, -1, 0], 'schur_index': 1}
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id: 15739148
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, -2, 2, 2, 2, 2, 0, -2, 0, 0, 0, -2, -2, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, -2, 0, -2, 0, 0, -2, 0, 0, 0, -1, 2, 0, 2, 2, 1, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, 1, 1, 1, -1, -1, 2, 0, 1, -1, 0, 1, -2, 0, 0, 1, 0, -1, 2, 2, -1, -1, 2, -1, -1, -1, 0, 1, 1, 0, 1, 0], 'schur_index': 1}
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id: 15739149
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, -1, -1, 2, 2, -1, -1, -2, -2, -2, -2, 0, -2, 0, 0, -2, 0, 0, 0, -1, 2, 0, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 1, -2, 0, -1, 1, 0, 1, 2, 0, 0, -1, 0, 1, -2, -2, 1, 1, -2, 1, 1, 1, 0, 1, 1, 0, 1, 0], 'schur_index': 1}
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id: 15739150
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 2, -2, -2, -2, -2, 0, 0, -2, 0, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739152
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -1, 2, -1, 2, -1, 2, -1, -2, -2, -2, 0, -2, 0, -2, -2, 0, 0, 0, 0, 2, -1, -1, -1, -1, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, -1, -2, 1, -1, 0, 1, 1, 0, 0, 2, -1, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1], 'schur_index': 1}
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id: 15739153
{'cdim': 3, 'counter': 21, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, -1, -1, 3, -1, 3, 3, -1, -1, 1, -1, -1, -1, -1, 3, 1, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, 3, -1, -1, 1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
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id: 15739154
{'cdim': 3, 'counter': 22, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, -1, 3, -1, -1, -1, -1, 3, 3, -1, 3, -1, 1, -1, -1, 3, -1, -1, 1, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 3, -1, 3, 3, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, -1, -1, 3, -1, 1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
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id: 15739155
{'cdim': 3, 'counter': 23, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, 3, -1, -1, 3, -1, -1, 3, 1, -1, -1, -1, 3, -1, 1, 1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 3, 3, 3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
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id: 15739156
{'cdim': 3, 'counter': 24, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, -1, -1, 3, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
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id: 15739157
{'cdim': 3, 'counter': 25, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, -1, 3, -1, -1, -1, -1, 3, 3, -1, 3, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 3, -1, 3, 3, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 15739158
{'cdim': 3, 'counter': 26, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 3, 3, 3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 15739159
{'cdim': 3, 'counter': 27, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, -1, -1, 3, -1, 1, -3, 1, 3, -3, 1, 1, -1, 1, 1, -1, -1, 3, 1, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -3, 3, -1, -3, 3, -1, -1, -1, -1, -1, 3, 1, -3, 1, 1, -3, 1, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 15739160
{'cdim': 3, 'counter': 28, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, -1, -1, 3, -1, 1, -3, 1, 3, -3, 1, 1, 1, 1, 1, -1, -1, 3, -1, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -3, 3, -1, -3, 3, -1, -1, -1, -1, -1, 3, 1, -3, 1, 1, -3, 1, -1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 15739161
{'cdim': 3, 'counter': 29, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, -1, 3, -1, -1, 1, 1, -3, 3, 1, -3, 1, -1, 1, 1, 3, -1, -1, 1, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -3, -1, 3, -3, -1, 3, -1, -1, -1, 3, -1, 1, 1, -3, 1, 1, -3, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
-
id: 15739163
{'cdim': 3, 'counter': 30, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, -1, 3, -1, -1, 1, 1, -3, 3, 1, -3, 1, 1, 1, 1, 3, -1, -1, -1, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -3, -1, 3, -3, -1, 3, -1, -1, -1, 3, -1, 1, 1, -3, 1, 1, -3, -1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
-
id: 15739164
{'cdim': 3, 'counter': 31, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -1, -1, -1, -3, 1, 1, 3, 1, 1, -3, -1, 1, 1, -1, 3, -1, 1, 1, -1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 3, 3, -3, -1, -1, -3, -1, -1, -1, -1, 3, -1, -1, -3, 1, 1, -3, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
-
id: 15739165
{'cdim': 3, 'counter': 32, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -1, -1, -1, -3, 1, 1, 3, 1, 1, -3, 1, 1, 1, -1, 3, -1, -1, -1, -1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 3, 3, -3, -1, -1, -3, -1, -1, -1, -1, 3, -1, -1, -3, 1, 1, -3, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 15739166
{'cdim': 3, 'counter': 33, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3m', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, -1, -1, 3, -1, 1, 3, 1, -3, -3, -1, -1, -1, 1, -1, 1, 1, -3, 1, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 3, 1, -3, 1, -1, 3, -1, -1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 15739167
{'cdim': 3, 'counter': 34, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3n', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, -1, -1, 3, -1, 1, 3, 1, -3, -3, -1, -1, 1, 1, -1, 1, 1, -3, -1, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -3, 3, -1, 3, 3, -1, -1, -1, -1, -1, 3, 1, -3, 1, -1, 3, -1, -1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15739168
{'cdim': 3, 'counter': 35, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3o', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, -1, 3, -1, -1, 1, -1, -3, -3, 1, 3, -1, -1, 1, -1, -3, 1, 1, 1, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -3, -1, 3, 3, -1, 3, -1, -1, -1, 3, -1, 1, 1, -3, -1, -1, 3, -1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15739169
{'cdim': 3, 'counter': 36, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3p', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, -1, 3, -1, -1, 1, -1, -3, -3, 1, 3, -1, 1, 1, -1, -3, 1, 1, -1, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -3, -1, 3, 3, -1, 3, -1, -1, -1, 3, -1, 1, 1, -3, -1, -1, 3, -1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 15739170
{'cdim': 3, 'counter': 37, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3q', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, 3, -1, -1, -1, -3, -1, 1, -3, 1, -1, 3, -1, 1, -1, 1, -3, 1, 1, -1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 3, 3, -3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
-
id: 15739171
{'cdim': 3, 'counter': 38, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3r', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, 3, 3, -1, -1, -1, -3, -1, 1, -3, 1, -1, 3, 1, 1, -1, 1, -3, 1, -1, 1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 3, 3, -3, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, -3, 1, 1, 3, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
-
id: 15739172
{'cdim': 3, 'counter': 39, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3s', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, 3, -1, -1, -3, -1, -3, 3, 1, 1, -1, -1, 1, 1, 1, -3, -1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 3, 3, -1, -3, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -3, 1, -1, -1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15739174
{'cdim': 3, 'counter': 40, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3t', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, -1, 3, -1, -1, -3, -1, -3, 3, 1, 1, 1, -1, 1, 1, 1, -3, 1, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 3, 3, -1, -3, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, 1, -3, 1, -1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 15739175
{'cdim': 3, 'counter': 41, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3u', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, 3, -1, -1, -1, 1, 3, -3, -1, -3, 1, -1, -1, 1, -3, 1, 1, -1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 3, -1, 3, -3, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, 1, 1, -3, -1, -1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
-
id: 15739176
{'cdim': 3, 'counter': 42, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3v', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, -1, 3, -1, -1, -1, 1, 3, -3, -1, -3, 1, 1, -1, 1, -3, 1, 1, 1, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 3, -1, 3, -3, -1, 3, -1, -1, -1, 3, -1, -1, -1, 3, 1, 1, -3, -1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
-
id: 15739177
{'cdim': 3, 'counter': 43, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3w', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, 3, -1, -1, -1, 3, 1, -1, -3, -1, 1, -3, -1, -1, 1, 1, -3, 1, -1, 1, 1, 1, 3, 3, 3, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 3, 3, 3, -1, -1, -3, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -3, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
-
id: 15739178
{'cdim': 3, 'counter': 44, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.3x', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -3, 3, -1, -1, -1, 3, 1, -1, -3, -1, 1, -3, 1, -1, 1, 1, -3, 1, 1, -1, 1, -1, 3, 3, 3, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 3, 3, 3, -1, -1, -3, -1, -1, -1, -1, 3, -1, -1, 3, -1, -1, -3, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
-
id: 15739179
{'cdim': 4, 'counter': 45, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, 0, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739180
{'cdim': 4, 'counter': 46, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739181
{'cdim': 4, 'counter': 47, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 4, 4, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739182
{'cdim': 4, 'counter': 48, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4d', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 4, 4, 4, -4, 0, -4, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 2, -2, -2, 0, 4, 4, 4, -2, -2, -2, -2, 2, 2, 2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739183
{'cdim': 4, 'counter': 49, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 0, -4, 4, 4, 4, 4, 0, -4, 0, 0, 0, -4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 4, 4, 2, -2, -2, -2, 4, -2, -2, -2, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739185
{'cdim': 4, 'counter': 50, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, -2, -2, 1, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, -2, -2, 0, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739186
{'cdim': 6, 'counter': 51, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, 6, -2, -2, -2, 2, -2, -2, -2, 6, -2, -2, -2, 0, 2, 2, -2, -2, -2, 0, 0, 2, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 6, -2, -2, 6, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739187
{'cdim': 6, 'counter': 52, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6b', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 0, 6, -2, -2, 6, -2, 0, 6, 0, 0, 0, -2, -2, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, -2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 1, -2, 0, 6, -2, -3, -3, 1, 1, -2, 1, 1, -3, 0, 0, 0, 1, -3, 1, 1, -1, 2, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 1, -2, 2, -1, 1, -2, 1, 1, -1, 0, 1, -1, 0, 1, 0], 'schur_index': 1}
-
id: 15739188
{'cdim': 6, 'counter': 53, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6c', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 0, 6, -2, 6, -2, -2, 0, -2, 0, 0, 0, 6, -2, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, -2, 2, 2, 0, -2, 0, 0, -2, 0, 0, 0, 1, -2, 0, -2, 6, -3, 1, -3, 1, -2, 1, -3, 1, 0, 0, 0, 1, 1, -3, 1, -1, 2, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 2, -2, 1, 1, -2, 1, -1, 1, 0, 1, 1, 0, -1, 0], 'schur_index': 1}
-
id: 15739189
{'cdim': 6, 'counter': 54, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6d', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 0, 6, 6, -2, -2, -2, 0, -2, 0, 0, 0, -2, 6, 2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, -2, -2, 0, 2, 0, 0, -2, 0, 0, 0, -3, 6, 0, -2, -2, -3, 1, 1, 1, -2, -3, 1, 1, 0, 0, 0, -3, 1, 1, 1, -1, 2, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 1, -2, -2, 1, -1, 2, -1, 1, 1, 0, -1, 1, 0, 1, 0], 'schur_index': 1}
-
id: 15739190
{'cdim': 6, 'counter': 55, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6e', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 6, -2, -2, 0, -2, 0, 6, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, -2, 0, 2, 0, -2, -2, 0, 0, 0, 0, -2, 1, -3, -3, 1, 0, 6, -2, -2, 1, 1, 1, -3, 1, -3, 1, 0, 0, 0, 1, 2, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 1, -1, 2, -2, 1, 1, 1, -1, 1, 0, 0, -1, 0, 1], 'schur_index': 1}
-
id: 15739191
{'cdim': 6, 'counter': 56, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6f', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, -2, 6, -2, -2, -2, 0, 6, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, -2, 2, 0, -2, 0, 2, -2, 0, 0, 0, 0, -2, 1, -3, 1, -3, 0, -2, 6, -2, 1, 1, -3, 1, 1, 1, -3, 0, 0, 0, 1, 2, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 2, -1, 1, -2, -2, 1, 1, -1, 1, 1, 0, 0, 1, 0, -1], 'schur_index': 1}
-
id: 15739192
{'cdim': 6, 'counter': 57, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6g', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, 0, 6, -2, -2, -2, 6, 0, -2, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, -2, 0, -2, 0, -2, 2, 0, 0, 0, 0, 6, -3, -3, 1, 1, 0, -2, -2, -2, 1, -3, 1, 1, -3, 1, 1, 0, 0, 0, 1, 2, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, 2, -1, -1, 1, 1, -1, 0, 0, 1, 0, 1], 'schur_index': 1}
-
id: 15739193
{'cdim': 6, 'counter': 58, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6h', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, -6, -6, -2, -2, -2, 2, 2, 2, 2, 6, 2, 2, 2, 0, -2, -2, -2, -2, -2, 0, 0, 2, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -6, -2, -2, -6, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739194
{'cdim': 6, 'counter': 59, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6i', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, -6, 6, -2, -2, -2, 2, 2, -2, 2, -6, 2, -2, -2, 0, -2, 2, 2, 2, 2, 0, 0, -2, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -6, -2, -2, 6, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739196
{'cdim': 6, 'counter': 60, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6j', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, 6, -6, -2, -2, -2, 2, -2, 2, -2, -6, -2, 2, 2, 0, 2, -2, 2, 2, 2, 0, 0, -2, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 6, -2, -2, -6, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 15739197
{'cdim': 6, 'counter': 61, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6k', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 0, 6, -2, -2, 6, -2, 0, 6, 0, 0, 0, -2, -2, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, 2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 1, -2, 0, 6, -2, -3, -3, 1, 1, -2, 1, 1, -3, 0, 0, 0, 1, -3, 1, 1, 1, -2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 2, -2, 1, -1, 2, -1, -1, 1, 0, -1, 1, 0, -1, 0], 'schur_index': 1}
-
id: 15739198
{'cdim': 6, 'counter': 62, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6l', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 0, 6, -2, 6, -2, -2, 0, -2, 0, 0, 0, 6, -2, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, 2, -2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 1, -2, 0, -2, 6, -3, 1, -3, 1, -2, 1, -3, 1, 0, 0, 0, 1, 1, -3, 1, 1, -2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, -2, 2, -1, -1, 2, -1, 1, -1, 0, -1, -1, 0, 1, 0], 'schur_index': 1}
-
id: 15739199
{'cdim': 6, 'counter': 63, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6m', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 0, 6, 6, -2, -2, -2, 0, -2, 0, 0, 0, -2, 6, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, 2, 2, 0, -2, 0, 0, 2, 0, 0, 0, -3, 6, 0, -2, -2, -3, 1, 1, 1, -2, -3, 1, 1, 0, 0, 0, -3, 1, 1, 1, 1, -2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 2, 2, -1, 1, -2, 1, -1, -1, 0, 1, -1, 0, -1, 0], 'schur_index': 1}
-
id: 15739200
{'cdim': 6, 'counter': 64, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6n', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, -2, -2, 6, -2, -2, 0, -2, 0, 6, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, 2, 0, -2, 0, 2, 2, 0, 0, 0, 0, -2, 1, -3, -3, 1, 0, 6, -2, -2, 1, 1, 1, -3, 1, -3, 1, 0, 0, 0, 1, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, -1, 1, -2, 2, -1, -1, -1, 1, -1, 0, 0, 1, 0, -1], 'schur_index': 1}
-
id: 15739201
{'cdim': 6, 'counter': 65, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6o', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, -2, 6, -2, -2, -2, 0, 6, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, 2, -2, 0, 2, 0, -2, 2, 0, 0, 0, 0, -2, 1, -3, 1, -3, 0, -2, 6, -2, 1, 1, -3, 1, 1, 1, -3, 0, 0, 0, 1, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 1, -1, 2, 2, -1, -1, 1, -1, -1, 0, 0, -1, 0, 1], 'schur_index': 1}
-
id: 15739202
{'cdim': 6, 'counter': 66, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6p', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, 0, 6, -2, -2, -2, 6, 0, -2, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 6, -3, -3, 1, 1, 0, -2, -2, -2, 1, -3, 1, 1, -3, 1, 1, 0, 0, 0, 1, -2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, -1, -1, 2, -2, 1, 1, -1, -1, 1, 0, 0, -1, 0, -1], 'schur_index': 1}
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id: 15739203
{'cdim': 6, 'counter': 67, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6q', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, -2, -2, 6, -2, 2, 0, 2, 0, -6, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, 2, 0, 2, 0, -2, -2, 0, 0, 0, 0, -2, 1, 3, -3, 1, 0, 6, -2, -2, 1, 1, 1, -3, -1, 3, -1, 0, 0, 0, 1, -2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 2, -1, 1, -2, 2, -1, -1, -1, 1, 1, 0, 0, -1, 0, 1], 'schur_index': 1}
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id: 15739204
{'cdim': 6, 'counter': 68, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6r', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, -2, -2, 6, -2, 2, 0, 2, 0, -6, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, -2, 0, -2, 0, 2, 2, 0, 0, 0, 0, -2, 1, 3, -3, 1, 0, 6, -2, -2, 1, 1, 1, -3, -1, 3, -1, 0, 0, 0, 1, 2, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 1, -1, 2, -2, 1, 1, 1, -1, -1, 0, 0, 1, 0, -1], 'schur_index': 1}
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id: 15739205
{'cdim': 6, 'counter': 69, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6s', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, -2, 6, -2, -2, 2, 0, -6, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, 2, -2, 0, -2, 0, 2, -2, 0, 0, 0, 0, -2, 1, 3, 1, -3, 0, -2, 6, -2, 1, 1, -3, 1, -1, -1, 3, 0, 0, 0, 1, -2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -2, 1, -1, 2, 2, -1, -1, 1, -1, 1, 0, 0, 1, 0, -1], 'schur_index': 1}
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id: 15739207
{'cdim': 6, 'counter': 70, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6t', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, -2, 6, -2, -2, 2, 0, -6, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, -2, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, -2, 1, 3, 1, -3, 0, -2, 6, -2, 1, 1, -3, 1, -1, -1, 3, 0, 0, 0, 1, 2, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 2, -1, 1, -2, -2, 1, 1, -1, 1, -1, 0, 0, -1, 0, 1], 'schur_index': 1}
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id: 15739208
{'cdim': 6, 'counter': 71, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6u', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, 6, -2, -2, -2, -6, 0, 2, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, 2, -2, 2, 0, -2, 0, -2, 2, 0, 0, 0, 0, 6, -3, 3, 1, 1, 0, -2, -2, -2, 1, -3, 1, 1, 3, -1, -1, 0, 0, 0, 1, -2, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 2, -1, -1, 2, -2, 1, 1, -1, -1, -1, 0, 0, 1, 0, 1], 'schur_index': 1}
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id: 15739209
{'cdim': 6, 'counter': 72, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6v', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, -6, 0, 6, -2, -2, -2, -6, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, -3, 6, -3, 0, 0, 0, 0, -2, 2, -2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 6, -3, 3, 1, 1, 0, -2, -2, -2, 1, -3, 1, 1, 3, -1, -1, 0, 0, 0, 1, 2, -1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 1, 1, -2, 2, -1, -1, 1, 1, 1, 0, 0, -1, 0, -1], 'schur_index': 1}
-
id: 15739210
{'cdim': 6, 'counter': 73, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6w', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, -2, -2, 6, -2, 0, -6, 0, 0, 0, 2, 2, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, 2, -2, 0, -2, 0, 0, 2, 0, 0, 0, 1, -2, 0, 6, -2, 3, -3, 1, 1, -2, 1, 1, -3, 0, 0, 0, -1, 3, -1, 1, 1, -2, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 2, -2, 1, -1, 2, -1, -1, 1, 0, 1, -1, 0, 1, 0], 'schur_index': 1}
-
id: 15739211
{'cdim': 6, 'counter': 74, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6x', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, -2, -2, 6, -2, 0, -6, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, -2, 2, 0, 2, 0, 0, -2, 0, 0, 0, 1, -2, 0, 6, -2, 3, -3, 1, 1, -2, 1, 1, -3, 0, 0, 0, -1, 3, -1, 1, -1, 2, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 1, -2, 2, -1, 1, -2, 1, 1, -1, 0, -1, 1, 0, -1, 0], 'schur_index': 1}
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id: 15739212
{'cdim': 6, 'counter': 75, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6y', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, -2, 6, -2, -2, 0, 2, 0, 0, 0, -6, 2, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, 2, -2, 2, 0, -2, 0, 0, -2, 0, 0, 0, 1, -2, 0, -2, 6, 3, 1, -3, 1, -2, 1, -3, 1, 0, 0, 0, -1, -1, 3, 1, 1, -2, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 1, -2, 2, -1, -1, 2, -1, 1, -1, 0, 1, 1, 0, -1, 0], 'schur_index': 1}
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id: 15739213
{'cdim': 6, 'counter': 76, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6z', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, -2, 6, -2, -2, 0, 2, 0, 0, 0, -6, 2, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, -2, 2, -2, 0, 2, 0, 0, 2, 0, 0, 0, 1, -2, 0, -2, 6, 3, 1, -3, 1, -2, 1, -3, 1, 0, 0, 0, -1, -1, 3, 1, -1, 2, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 2, -2, 1, 1, -2, 1, -1, 1, 0, -1, -1, 0, 1, 0], 'schur_index': 1}
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id: 15739214
{'cdim': 6, 'counter': 77, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6aa', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, 6, -2, -2, -2, 0, 2, 0, 0, 0, 2, -6, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 6, -3, -3, 0, 0, 0, 0, 2, -2, 2, -2, 0, 2, 0, 0, -2, 0, 0, 0, -3, 6, 0, -2, -2, 3, 1, 1, 1, -2, -3, 1, 1, 0, 0, 0, 3, -1, -1, 1, 1, -2, 0, -1, 1, 0, -1, 0, 0, 0, 0, 0, -1, 2, 2, -1, 1, -2, 1, -1, -1, 0, -1, 1, 0, 1, 0], 'schur_index': 1}
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id: 15739215
{'cdim': 6, 'counter': 78, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.6ab', 'multiplicity': 1, 'nt': [18, 111], 'qdim': 6, 'qvalues': [6, 0, -6, 6, -2, -2, -2, 0, 2, 0, 0, 0, 2, -6, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, 6, -3, -3, 0, 0, 0, 0, -2, 2, -2, 2, 0, -2, 0, 0, 2, 0, 0, 0, -3, 6, 0, -2, -2, 3, 1, 1, 1, -2, -3, 1, 1, 0, 0, 0, 3, -1, -1, 1, -1, 2, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 1, -2, -2, 1, -1, 2, -1, 1, 1, 0, 1, -1, 0, -1, 0], 'schur_index': 1}
-
id: 15739216
{'cdim': 8, 'counter': 79, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, -4, -4, 0, -4, -4, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739218
{'cdim': 12, 'counter': 80, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12a', 'multiplicity': 1, 'nt': [24, 1502], 'qdim': 12, 'qvalues': [12, 0, 12, -4, -4, -4, 4, 0, -4, 0, 0, 0, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, -4, -4, -6, 2, 2, -2, 4, 2, 2, 2, 0, 0, 0, 2, 2, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739219
{'cdim': 12, 'counter': 81, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12b', 'multiplicity': 1, 'nt': [24, 1502], 'qdim': 12, 'qvalues': [12, 12, 0, -4, -4, -4, 4, -4, 0, -4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, -6, 2, 2, 0, -4, -4, 4, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739220
{'cdim': 12, 'counter': 82, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12c', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 0, 0, -4, -4, 12, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -6, 2, 0, -6, 2, 2, 2, -1, -1, 3, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 2, -1, -1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739221
{'cdim': 12, 'counter': 83, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12d', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 0, 0, -4, 12, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, -6, 0, 2, -6, 2, 2, -1, 3, -1, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, -1, 1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739222
{'cdim': 12, 'counter': 84, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12e', 'multiplicity': 1, 'nt': [24, 2661], 'qdim': 12, 'qvalues': [12, 0, 0, 12, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 2, 2, 0, 2, 2, 2, 2, 3, -1, -1, 0, 0, 0, 0, 0, 0, -1, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739223
{'cdim': 12, 'counter': 85, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12f', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 0, 0, -4, -4, 12, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -6, 2, 0, -6, 2, 2, 2, -1, -1, 3, 0, 0, 0, 0, 0, 0, -1, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, -2, 1, 1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739224
{'cdim': 12, 'counter': 86, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12g', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 0, 0, -4, 12, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, -6, 0, 2, -6, 2, 2, -1, 3, -1, 0, 0, 0, 0, 0, 0, -1, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 1, -1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739225
{'cdim': 12, 'counter': 87, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12h', 'multiplicity': 1, 'nt': [36, 1364], 'qdim': 12, 'qvalues': [12, 0, 0, 12, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 0, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 0, 2, 2, 0, 2, 2, 2, 2, 3, -1, -1, 0, 0, 0, 0, 0, 0, -1, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, -1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739226
{'cdim': 12, 'counter': 88, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12i', 'multiplicity': 1, 'nt': [36, 1674], 'qdim': 12, 'qvalues': [12, -12, 0, -4, -4, -4, 4, 4, 0, 4, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 6, 2, 2, 0, -4, -4, 4, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739227
{'cdim': 12, 'counter': 89, 'faithful': False, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.12j', 'multiplicity': 1, 'nt': [36, 1674], 'qdim': 12, 'qvalues': [12, 0, -12, -4, -4, -4, 4, 0, 4, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, -4, -4, 6, 2, 2, -2, 4, 2, 2, 2, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 15739229
{'cdim': 24, 'counter': 90, 'faithful': True, 'group': '3456.oc', 'group_order': 3456, 'image': None, 'label': '3456.oc.24a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 4, 4, -4, -4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 35701977
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 3456, 'label': '3456.oc.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35701988
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id: 35701999
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 1728, 'label': '3456.oc.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35702010
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 1728, 'label': '3456.oc.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702021
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 1728, 'label': '3456.oc.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702032
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 1728, 'label': '3456.oc.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702043
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 1728, 'label': '3456.oc.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702054
{'center': '1.a1', 'center_index': 1, 'center_order': 3456, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 1728, 'label': '3456.oc.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35702065
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 576, 'label': '3456.oc.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35701978
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 576, 'label': '3456.oc.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35701979
{'center': '6.b1', 'center_index': 6, 'center_order': 576, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 576, 'label': '3456.oc.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35701980
{'center': '6.b1', 'center_index': 6, 'center_order': 576, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 288, 'label': '3456.oc.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35701981
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1', 'kernel_order': 288, 'label': '3456.oc.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35701982
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 288, 'label': '3456.oc.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35701983
{'center': '6.b1', 'center_index': 6, 'center_order': 576, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 288, 'label': '3456.oc.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35701984
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1', 'kernel_order': 288, 'label': '3456.oc.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35701985
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1', 'kernel_order': 288, 'label': '3456.oc.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35701986
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 288, 'label': '3456.oc.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35701987
{'center': '6.b1', 'center_index': 6, 'center_order': 576, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 288, 'label': '3456.oc.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35701989
{'center': '6.a1', 'center_index': 6, 'center_order': 576, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 288, 'label': '3456.oc.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35701990
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 21, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 144, 'label': '3456.oc.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35701991
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 22, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 144, 'label': '3456.oc.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35701992
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 23, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 144, 'label': '3456.oc.3c', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35701993
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 24, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 144, 'label': '3456.oc.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35701994
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 144, 'label': '3456.oc.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35701995
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id: 35701996
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id: 35701997
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 72, 'label': '3456.oc.3h', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35701998
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 29, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 72, 'label': '3456.oc.3i', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35702000
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 30, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 72, 'label': '3456.oc.3j', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35702001
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 31, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 72, 'label': '3456.oc.3k', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 35702002
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 32, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1', 'kernel_order': 72, 'label': '3456.oc.3l', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 35702003
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 33, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3m', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702004
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 34, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3n', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702005
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 35, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3o', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702006
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 36, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3p', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702007
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 37, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3q', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702008
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 38, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3r', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702009
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 39, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3s', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
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id: 35702011
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 40, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3t', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702012
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 41, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3u', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
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id: 35702013
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 42, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3v', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
-
id: 35702014
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 43, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3w', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
-
id: 35702015
{'center': '24.a1', 'center_index': 24, 'center_order': 144, 'counter': 44, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 72, 'label': '3456.oc.3x', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
-
id: 35702016
{'center': '36.b1', 'center_index': 36, 'center_order': 96, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1', 'kernel_order': 96, 'label': '3456.oc.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702017
{'center': '36.a1', 'center_index': 36, 'center_order': 96, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 96, 'label': '3456.oc.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 35702018
{'center': '36.a1', 'center_index': 36, 'center_order': 96, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 96, 'label': '3456.oc.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 35702019
{'center': '36.a1', 'center_index': 36, 'center_order': 96, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 48, 'label': '3456.oc.4d', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 35702020
{'center': '36.a1', 'center_index': 36, 'center_order': 96, 'counter': 49, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 48, 'label': '3456.oc.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702022
{'center': '36.b1', 'center_index': 36, 'center_order': 96, 'counter': 50, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1', 'kernel_order': 48, 'label': '3456.oc.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702023
{'center': '96.a1', 'center_index': 96, 'center_order': 36, 'counter': 51, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '96.227', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1', 'kernel_order': 36, 'label': '3456.oc.6a', 'nt': [8, 34], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702051
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 77, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6aa', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702052
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 78, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6ab', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702024
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 52, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6b', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702025
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 53, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6c', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702026
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 54, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6d', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702027
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 55, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6e', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702028
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 56, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6f', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702029
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 57, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6g', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702030
{'center': '96.a1', 'center_index': 96, 'center_order': 36, 'counter': 58, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.b1', 'kernel_order': 18, 'label': '3456.oc.6h', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702031
{'center': '96.a1', 'center_index': 96, 'center_order': 36, 'counter': 59, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1', 'kernel_order': 18, 'label': '3456.oc.6i', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702033
{'center': '96.a1', 'center_index': 96, 'center_order': 36, 'counter': 60, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '192.1538', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1', 'kernel_order': 18, 'label': '3456.oc.6j', 'nt': [12, 100], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702034
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 61, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6k', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702035
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 62, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6l', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702036
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 63, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6m', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702037
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 64, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6n', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702038
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 65, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6o', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702039
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 66, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 24, 'label': '3456.oc.6p', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702040
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 67, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6q', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702041
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 68, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6r', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702042
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 69, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6s', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702044
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 70, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6t', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702045
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 71, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6u', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
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id: 35702046
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 72, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6v', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
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id: 35702047
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 73, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6w', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702048
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 74, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6x', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702049
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 75, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6y', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
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id: 35702050
{'center': '144.a1', 'center_index': 144, 'center_order': 24, 'counter': 76, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '288.1028', 'image_order': 288, 'indicator': 1, 'kernel': '288.a1', 'kernel_order': 12, 'label': '3456.oc.6z', 'nt': [18, 111], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
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id: 35702053
{'center': '216.a1', 'center_index': 216, 'center_order': 16, 'counter': 79, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '216.162', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 16, 'label': '3456.oc.8a', 'nt': [12, 117], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702055
{'center': '576.a1', 'center_index': 576, 'center_order': 6, 'counter': 80, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '576.8660', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 6, 'label': '3456.oc.12a', 'nt': [24, 1502], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702056
{'center': '576.a1', 'center_index': 576, 'center_order': 6, 'counter': 81, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '576.8660', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1', 'kernel_order': 6, 'label': '3456.oc.12b', 'nt': [24, 1502], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702057
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 82, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12c', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702058
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 83, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12d', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702059
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 84, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12e', 'nt': [24, 2661], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702060
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 85, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12f', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702061
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 86, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12g', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[-6, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702062
{'center': '864.a1', 'center_index': 864, 'center_order': 4, 'counter': 87, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '864.4673', 'image_order': 864, 'indicator': 1, 'kernel': '864.a1', 'kernel_order': 4, 'label': '3456.oc.12h', 'nt': [36, 1364], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702063
{'center': '576.a1', 'center_index': 576, 'center_order': 6, 'counter': 88, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '1152.157864', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 3, 'label': '3456.oc.12i', 'nt': [36, 1674], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702064
{'center': '576.a1', 'center_index': 576, 'center_order': 6, 'counter': 89, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '1152.157864', 'image_order': 1152, 'indicator': 1, 'kernel': '1152.a1', 'kernel_order': 3, 'label': '3456.oc.12j', 'nt': [36, 1674], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-12, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 35702066
{'center': '3456.a1', 'center_index': 3456, 'center_order': 1, 'counter': 90, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3456.oc', 'group_counter': 367, 'group_order': 3456, 'image': None, 'image_isoclass': '3456.oc', 'image_order': 3456, 'indicator': 1, 'kernel': '3456.a1', 'kernel_order': 1, 'label': '3456.oc.24a', 'nt': [48, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-12, 0]], [[-12, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 201935329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3456, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '3456.oc.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3456.oc', 'subgroup_hash': 1942231094641922994, 'subgroup_order': 3456, 'subgroup_tex': 'D_6^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 201935812
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1728, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47897', 'subgroup_hash': 47897, 'subgroup_order': 1728, 'subgroup_tex': 'C_3\\times C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 201935923
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1728, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47899', 'subgroup_hash': 47899, 'subgroup_order': 1728, 'subgroup_tex': '(C_6\\times D_6):S_4', 'supersolvable': False, 'sylow': 0}
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id: 201936034
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1728, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47902', 'subgroup_hash': 47902, 'subgroup_order': 1728, 'subgroup_tex': 'D_6^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 201936145
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1728, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47898', 'subgroup_hash': 47898, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 201936256
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1728, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.47900', 'subgroup_hash': 47900, 'subgroup_order': 1728, 'subgroup_tex': 'C_6^2:(C_2\\times S_4)', 'supersolvable': False, 'sylow': 0}
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id: 201936367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 576, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.157864', 'subgroup_hash': 8514248756003452164, 'subgroup_order': 1152, 'subgroup_tex': 'C_2^5:S_3^2', 'supersolvable': False, 'sylow': 0}
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id: 201936478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 576, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1152.134261', 'subgroup_hash': 7928613971095736285, 'subgroup_order': 1152, 'subgroup_tex': 'D_6^2:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936589
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4713', 'subgroup_hash': 4713, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times D_6):A_4', 'supersolvable': False, 'sylow': 0}
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id: 201935330
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 864, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4714', 'subgroup_hash': 4714, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:(C_2\\times A_4)', 'supersolvable': False, 'sylow': 0}
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id: 201935441
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 864, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4708', 'subgroup_hash': 4708, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 201935552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 864, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4709', 'subgroup_hash': 4709, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935663
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 864, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4710', 'subgroup_hash': 4710, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935746
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.4.f1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '864.4673', 'subgroup_hash': 4673, 'subgroup_order': 864, 'subgroup_tex': 'S_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935757
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 576, 'counter': 15, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3456.oc.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935768
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 576, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '576.8675', 'subgroup_hash': 8675, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935779
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8670', 'subgroup_hash': 8670, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:S_4\\times C_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935790
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8671', 'subgroup_hash': 8671, 'subgroup_order': 576, 'subgroup_tex': '(C_2^2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935801
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7159', 'subgroup_hash': 7159, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935813
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.6139', 'subgroup_hash': 6139, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 288, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7567', 'subgroup_hash': 7567, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935835
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935846
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935857
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7405', 'subgroup_hash': 7405, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935868
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8673', 'subgroup_hash': 8673, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935879
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8553', 'subgroup_hash': 8553, 'subgroup_order': 576, 'subgroup_tex': 'C_4:D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935890
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.6134', 'subgroup_hash': 6134, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935901
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7160', 'subgroup_hash': 7160, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935912
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.6140', 'subgroup_hash': 6140, 'subgroup_order': 576, 'subgroup_tex': 'D_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935924
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935935
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 96, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935946
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 288, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8660', 'subgroup_hash': 8660, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935957
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7941', 'subgroup_hash': 7941, 'subgroup_order': 576, 'subgroup_tex': 'C_6^2.C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935968
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.6.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.7409', 'subgroup_hash': 7409, 'subgroup_order': 576, 'subgroup_tex': 'C_2^4:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935979
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 432, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.771', 'subgroup_hash': 771, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935990
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 72, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.745', 'subgroup_hash': 745, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 201936001
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.747', 'subgroup_hash': 747, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201936012
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 144, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201936023
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.749', 'subgroup_hash': 749, 'subgroup_order': 432, 'subgroup_tex': 'A_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201936035
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.746', 'subgroup_hash': 746, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
-
id: 201936046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.748', 'subgroup_hash': 748, 'subgroup_order': 432, 'subgroup_tex': 'A_4:S_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201936057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.20163', 'subgroup_hash': 20163, 'subgroup_order': 384, 'subgroup_tex': 'C_2^2\\wr S_3', 'supersolvable': False, 'sylow': 0}
-
id: 201936068
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '384.18491', 'subgroup_hash': 18491, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936079
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936090
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 288, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1043', 'subgroup_hash': 1043, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936101
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 288, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1044', 'subgroup_hash': 1044, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936112
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 288, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936123
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 288, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936134
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1042', 'subgroup_hash': 1042, 'subgroup_order': 288, 'subgroup_tex': 'C_2^5:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201936146
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936157
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936168
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936179
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936190
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.951', 'subgroup_hash': 951, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936201
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.568', 'subgroup_hash': 568, 'subgroup_order': 288, 'subgroup_tex': 'D_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.992', 'subgroup_hash': 992, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936223
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.976', 'subgroup_hash': 976, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936234
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.651', 'subgroup_hash': 651, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936245
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.616', 'subgroup_hash': 616, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936257
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936268
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 96, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936279
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936290
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936301
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936312
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936323
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936334
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.950', 'subgroup_hash': 950, 'subgroup_order': 288, 'subgroup_tex': 'C_2.D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936345
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936356
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936368
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.958', 'subgroup_hash': 958, 'subgroup_order': 288, 'subgroup_tex': 'D_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.952', 'subgroup_hash': 952, 'subgroup_order': 288, 'subgroup_tex': 'D_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.569', 'subgroup_hash': 569, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2.C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.631', 'subgroup_hash': 631, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.570', 'subgroup_hash': 570, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.571', 'subgroup_hash': 571, 'subgroup_order': 288, 'subgroup_tex': 'D_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.708', 'subgroup_hash': 708, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936467
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.653', 'subgroup_hash': 653, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936479
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.624', 'subgroup_hash': 624, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.625', 'subgroup_hash': 625, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1040', 'subgroup_hash': 1040, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936512
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1007', 'subgroup_hash': 1007, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.977', 'subgroup_hash': 977, 'subgroup_order': 288, 'subgroup_tex': 'D_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.737', 'subgroup_hash': 737, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.622', 'subgroup_hash': 622, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.794', 'subgroup_hash': 794, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.629', 'subgroup_hash': 629, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.739', 'subgroup_hash': 739, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936590
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936601
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1038', 'subgroup_hash': 1038, 'subgroup_order': 288, 'subgroup_tex': 'S_3\\times C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936612
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.817', 'subgroup_hash': 817, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 96, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936634
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 144, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936645
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 48, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1035', 'subgroup_hash': 1035, 'subgroup_order': 288, 'subgroup_tex': 'C_3\\times C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936656
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.724', 'subgroup_hash': 724, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936689
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.810', 'subgroup_hash': 810, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 48, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.12.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1036', 'subgroup_hash': 1036, 'subgroup_order': 288, 'subgroup_tex': '(C_2\\times C_6):S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 72, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.166', 'subgroup_hash': 166, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935375
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.162', 'subgroup_hash': 162, 'subgroup_order': 216, 'subgroup_tex': 'S_3^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935386
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.163', 'subgroup_hash': 163, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.164', 'subgroup_hash': 164, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935419
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935430
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.167', 'subgroup_hash': 167, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1358', 'subgroup_hash': 1358, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1046', 'subgroup_hash': 1046, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935464
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1410', 'subgroup_hash': 1410, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935475
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 96, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935486
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1399', 'subgroup_hash': 1399, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935519
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1540', 'subgroup_hash': 1540, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\wr C_3', 'supersolvable': False, 'sylow': 0}
-
id: 201935530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1043', 'subgroup_hash': 1043, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935597
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 96, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1542', 'subgroup_hash': 1542, 'subgroup_order': 192, 'subgroup_tex': 'D_6\\times C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935608
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935619
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 96, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935641
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935652
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935675
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.18.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1147', 'subgroup_hash': 1147, 'subgroup_order': 192, 'subgroup_tex': 'C_2^4:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935686
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 144, 'counter': 132, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935697
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 144, 'counter': 133, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 144, 'counter': 134, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.197', 'subgroup_hash': 197, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935719
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935730
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935741
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935744
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935745
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935747
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935748
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935749
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935750
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935751
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935752
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935753
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935754
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935755
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935756
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935758
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935759
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935760
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935761
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935762
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 24, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935763
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935764
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935765
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935766
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935767
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935769
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935770
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935771
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935772
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 24, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935773
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
-
id: 201935774
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935775
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935776
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935777
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935778
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 36, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935780
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935781
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935782
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935783
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935784
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935785
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935786
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935789
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935791
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935793
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935794
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935795
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935797
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935798
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935799
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.143', 'subgroup_hash': 143, 'subgroup_order': 144, 'subgroup_tex': 'C_4\\times S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201935800
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935802
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935804
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.145', 'subgroup_hash': 145, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935805
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935806
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935807
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935808
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935809
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935810
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935811
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935816
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201935818
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.150', 'subgroup_hash': 150, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935819
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935822
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935823
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935825
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935826
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935831
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935832
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935833
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935834
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.169', 'subgroup_hash': 169, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935836
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.149', 'subgroup_hash': 149, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.172', 'subgroup_hash': 172, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935838
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.154', 'subgroup_hash': 154, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dk2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dk2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935841
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.170', 'subgroup_hash': 170, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.95', 'subgroup_hash': 95, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935843
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.65', 'subgroup_hash': 65, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935844
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.195', 'subgroup_hash': 195, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935845
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.179', 'subgroup_hash': 179, 'subgroup_order': 144, 'subgroup_tex': 'C_4:C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935848
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.196', 'subgroup_hash': 196, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935849
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935850
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.177', 'subgroup_hash': 177, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935851
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935852
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935854
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935855
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 48, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935856
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.194', 'subgroup_hash': 194, 'subgroup_order': 144, 'subgroup_tex': 'C_2^4:C_3^2', 'supersolvable': False, 'sylow': 0}
-
id: 201935858
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935859
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.24.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935860
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '3456.oc.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.2163', 'subgroup_hash': 2163, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 2}
-
id: 201935861
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935862
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935863
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935865
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935866
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935867
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.40', 'subgroup_hash': 40, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935869
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 96, 'counter': 250, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935870
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 96, 'counter': 251, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3456.oc.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935871
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935872
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935873
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935874
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935875
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935876
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.134', 'subgroup_hash': 134, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2.D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935877
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935878
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.162', 'subgroup_hash': 162, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935881
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.159', 'subgroup_hash': 159, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935882
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935883
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.231', 'subgroup_hash': 231, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935884
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935885
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935886
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935887
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935888
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935889
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935891
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935893
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935894
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935895
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935896
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935897
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935898
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935899
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935900
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935902
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935903
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935904
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935905
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935906
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935907
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935908
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935909
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935910
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935911
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935913
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935914
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935915
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935916
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935917
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935918
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935919
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935920
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935921
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935922
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935925
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935926
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935927
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935928
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935929
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935930
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935931
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935932
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935933
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935934
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935937
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.144', 'subgroup_hash': 144, 'subgroup_order': 96, 'subgroup_tex': 'D_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935938
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935939
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935940
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.89', 'subgroup_hash': 89, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935941
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935942
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 48, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935943
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935944
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 48, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935945
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 16, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.167', 'subgroup_hash': 167, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935948
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935949
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935950
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935951
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935952
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.160', 'subgroup_hash': 160, 'subgroup_order': 96, 'subgroup_tex': 'C_2^4:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935953
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935954
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935955
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 16, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.36.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935956
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 72, 'counter': 329, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935958
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 72, 'counter': 330, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935959
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935960
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935961
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935962
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935963
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935964
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935965
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201935966
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935967
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935969
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935970
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935971
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935972
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935973
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 24, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935974
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 18, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935975
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935976
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935977
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935978
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935980
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 6, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935981
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935982
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935983
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935984
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 36, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935985
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935986
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935987
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935988
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935989
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935991
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935992
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935994
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201935995
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201935996
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935997
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935998
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935999
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936000
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936002
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936003
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bn3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936004
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bn4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936005
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936006
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936007
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936008
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936010
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936011
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936013
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936014
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bv2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936015
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936016
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936017
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936018
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936019
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936020
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936021
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936022
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936024
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936025
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936026
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936027
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936029
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936032
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936033
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936036
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936037
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936038
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936039
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936040
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936041
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936042
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936043
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936044
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936045
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936047
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936048
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936049
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936050
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936051
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936052
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936053
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
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id: 201936054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936056
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 36, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936058
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.df2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.df2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 12, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936062
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936063
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936065
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936066
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936067
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936070
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936071
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936072
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936073
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936074
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 36, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936075
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936076
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936077
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936078
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936080
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936081
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936082
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936083
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936084
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936085
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936086
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936087
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936088
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936089
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936091
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936092
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.48.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936093
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936094
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936095
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 16, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936096
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936097
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936098
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.193', 'subgroup_hash': 193, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936099
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
-
id: 201936100
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936104
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936105
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936106
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936107
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936108
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936109
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936110
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 48, 'counter': 468, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936111
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 48, 'counter': 469, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936115
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936116
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936117
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936118
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936119
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936120
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936121
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936122
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936124
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936125
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936126
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936127
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936128
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936129
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936130
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936131
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936132
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936133
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936135
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936136
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201936137
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936138
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936139
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936140
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936141
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936142
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936143
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936144
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936147
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936148
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936149
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936150
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936151
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936152
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936153
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936154
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936155
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936156
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936158
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936160
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936161
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936162
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936163
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936164
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936165
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936166
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bw2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936167
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936169
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936170
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936171
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936172
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936173
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936174
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 24, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936175
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936176
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936178
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936180
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936181
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936182
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936183
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936184
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936185
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936187
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936188
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936189
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936191
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936196
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936198
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936199
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936200
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936202
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936203
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936204
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936205
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936206
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936207
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936209
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936210
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936211
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936214
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936215
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936216
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936217
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936218
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936219
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936220
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936221
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936222
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936224
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936225
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936226
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936227
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936229
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936232
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936233
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936235
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936236
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936238
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936241
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936242
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936243
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936244
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.en2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.en2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936246
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936247
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eo2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eo2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936249
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936252
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936253
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936255
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936258
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936259
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936260
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936261
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936262
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936263
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936264
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936266
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936267
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936270
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936271
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936272
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 613, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936273
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 614, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936274
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936275
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 616, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936276
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936277
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936278
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936281
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936282
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936283
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936284
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936285
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936286
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936289
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936294
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 16, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936295
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 16, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936296
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 16, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936297
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936298
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.72.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936299
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 96, 'characteristic': True, 'core_order': 36, 'counter': 638, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3456.oc.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 36, 'counter': 639, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.96.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.226', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936302
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936303
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936304
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 18, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936305
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936306
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936307
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936308
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936309
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936310
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936311
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 6, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936313
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936314
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936315
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936316
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936317
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936318
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 9, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.q2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936319
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936320
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936321
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936322
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936324
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936325
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936326
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936327
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936328
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936329
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936330
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936331
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936332
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936333
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936335
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936336
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 9, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936337
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936338
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936339
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936340
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936341
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936342
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936343
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936344
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936346
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936347
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936348
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936349
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936350
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 201936351
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936352
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936353
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936354
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936355
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936357
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 18, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936358
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936359
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.bz2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.bz2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936360
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936361
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936362
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936363
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936364
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936365
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 18, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936366
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936369
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936370
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936371
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201936372
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.96.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201936373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936374
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936375
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936376
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936377
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936384
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936385
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 16, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936387
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936389
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936392
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
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id: 201936393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936394
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 201936395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 201936406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 734, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 735, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
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id: 201936408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 736, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 737, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936410
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936413
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 741, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 742, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936416
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 743, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
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id: 201936417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 16, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 16, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936419
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.108.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
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id: 201936420
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '3456.oc.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
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id: 201936421
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 748, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936422
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936425
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936426
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936428
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936429
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936430
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936431
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936432
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936433
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936436
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936437
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936438
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936439
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936440
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936441
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936442
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936446
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936447
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936448
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936451
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936452
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936453
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936455
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936457
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936458
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936459
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936460
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936461
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936462
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936465
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936466
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936468
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936469
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936472
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936473
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936474
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936475
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936477
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936481
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936485
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936486
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936489
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936491
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936496
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936497
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936498
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936502
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936503
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cr2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cr2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936508
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936509
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cu2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cu2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936510
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936511
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936513
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936515
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936516
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936517
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936518
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.db2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.db2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936519
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936520
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936521
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936522
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936524
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936525
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936526
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936527
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936528
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936529
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936530
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936533
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936535
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ds1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ds1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.dt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.du1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.du1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.dz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.dz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ea1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ea1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936549
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ec1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ec1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ed1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ed1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936552
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ee1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ee1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936553
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ef1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ef1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936554
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 868, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 869, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 870, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ei1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ei1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 3, 'counter': 871, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ej1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ej1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 872, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ek1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ek1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936560
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 873, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.el1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.el1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936561
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 874, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.em1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.em1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936562
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 875, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.en1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.en1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936563
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 876, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936564
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ep1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ep1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936565
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936566
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.er1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.er1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936568
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.es1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.es1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936569
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.et1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.et1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936570
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.eu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.eu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ev1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ev1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ew1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ew1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936573
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ex1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ex1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ex2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ex2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936575
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ey1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ey1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936576
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ey2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ey2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ez1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ez1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936579
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fa1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fa1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936580
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fa2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fa2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936581
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936582
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936585
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fe1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fe1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936586
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ff1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ff1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fg1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936588
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 12, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936591
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936592
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936593
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fi2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fi2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936595
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 201936599
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936602
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fr1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936604
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
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id: 201936605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ft1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ft1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936606
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936607
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936608
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936609
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.fx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201936610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936611
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.fz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.fz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936613
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ga1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ga1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 201936614
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936615
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 12, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936616
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936617
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.ge1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ge1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936618
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936619
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936620
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936621
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936622
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936624
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936625
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936626
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936627
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936628
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.go1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.go1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936629
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936630
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936631
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.gr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936632
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936633
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201936635
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 940, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936636
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 941, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936637
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 942, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201936638
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 943, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936639
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 944, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936640
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 945, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.144.gz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.gz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 201936641
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 18, 'counter': 946, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.192.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936642
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 18, 'counter': 947, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.192.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936643
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936644
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936646
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 6, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936647
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 9, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936648
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 9, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 9, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936650
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936651
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201936653
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936654
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936655
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 9, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936657
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 9, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936658
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936659
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936660
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 9, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936661
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936662
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 9, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936663
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201936664
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 967, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936665
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 9, 'counter': 968, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936666
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936668
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.192.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '192.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
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id: 201936669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 16, 'counter': 971, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936673
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936674
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936675
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936677
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 979, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936679
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 980, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936680
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 981, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936681
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 982, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 985, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936685
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 986, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201936687
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 989, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 990, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201936691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936693
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936694
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 994, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936695
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 995, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201936696
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936697
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 997, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201936698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201936699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935332
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1000, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bb2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bb2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935333
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1001, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935334
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935335
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935336
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1004, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1005, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935338
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935339
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935341
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935344
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1015, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935349
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1016, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1017, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1018, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935355
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935356
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935358
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935359
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935360
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1027, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935362
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935363
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935365
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935366
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1033, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1034, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935374
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935378
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1043, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935380
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1044, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935382
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935383
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935384
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1049, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935387
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1050, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cy2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cy2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1055, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935393
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 1056, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935394
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1057, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935396
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
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id: 201935398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1062, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935403
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935404
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.216.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 201935405
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 12, 'counter': 1067, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.288.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '288.1028', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1028, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935406
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935409
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935410
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935411
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935412
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935413
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935414
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935415
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935416
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935417
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935418
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935420
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 6, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935421
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935422
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 6, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935423
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935424
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 6, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935428
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935429
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.v2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.v2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935431
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935432
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935433
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935434
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1093, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935435
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1094, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1095, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935437
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1096, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935438
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1097, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935439
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1098, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935440
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1099, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935445
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bg2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bg2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935446
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935447
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bh2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bh2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935448
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935451
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935452
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935455
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201935456
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201935457
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935458
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935459
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 201935460
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935461
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935462
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935463
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 1119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935465
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935466
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bx2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.bx2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 1122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 201935468
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 1123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 201935469
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 1124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
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id: 201935470
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935471
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935472
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935473
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935474
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935477
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935478
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935479
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935481
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935482
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935483
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935484
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935485
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935488
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935489
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935490
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 1143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 201935491
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935492
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935494
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935495
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935496
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935498
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935502
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935503
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935507
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935509
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935510
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935511
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935512
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935513
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935514
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.do1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.do1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935515
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.288.dp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.dp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
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id: 201935516
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 9, 'counter': 1167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.384.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '384.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '384.20163', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20163, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201935517
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 1168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.384.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935518
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 1169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.384.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935520
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.384.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935521
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.384.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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id: 201935522
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935523
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935524
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935525
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935526
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935527
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935528
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935529
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935531
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935532
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935533
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 1182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935534
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935535
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935536
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935537
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935538
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935539
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935542
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935543
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935545
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935546
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935548
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935549
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935554
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935555
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935556
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935558
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935559
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935560
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.be3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935561
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.be4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.be4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935562
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935563
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935568
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935569
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935570
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bm2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bm2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935573
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bn2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bn2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935574
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935576
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935577
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935578
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935579
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935580
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935582
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 1229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935590
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935591
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935592
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935593
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ch1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ch1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 201935596
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ci1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ci1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935598
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935599
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ck1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ck1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935600
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935602
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935603
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 1245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.co1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.co1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935604
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.co2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.co2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935605
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935606
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cp2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cp2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935609
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cr1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cr1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935610
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 1251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935611
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cs2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cs2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935612
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.ct1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.ct1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935613
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935614
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
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id: 201935615
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935616
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cx1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935617
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cy1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cy1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935618
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.cz1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.cz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 4, 'counter': 1260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.da1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.da1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935621
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.db1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.db1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935622
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935623
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935624
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935625
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.de1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.de1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 201935626
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.df1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.df1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935627
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935628
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935629
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.di1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.di1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935631
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935633
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.432.dn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.dn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 201935636
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 576, 'characteristic': False, 'core_order': 6, 'counter': 1275, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '3456.oc.576.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '576.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '576.8660', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8660, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935637
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 1276, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935638
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1277, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935639
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 1278, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935640
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 3, 'counter': 1279, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935642
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935643
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 3, 'counter': 1281, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935644
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 1282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935645
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 201935646
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935647
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935648
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 3, 'counter': 1286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935649
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935650
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1288, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935651
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935653
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 1290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935654
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935655
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 3, 'counter': 1292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935656
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 3, 'counter': 1293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935657
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935658
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1295, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.576.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 201935659
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 1296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935660
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 1297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935661
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 1298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935662
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 3, 'counter': 1299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935665
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 1300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935666
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 1301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935667
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 1302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935668
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 1303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935669
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 1304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935670
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 1305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.576.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
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id: 201935671
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 4, 'counter': 1306, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3456.oc.864.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '864.4673', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4673, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935673
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935674
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935677
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935678
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935680
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935681
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935684
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935685
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935687
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935689
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.p2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.p2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935693
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935694
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1327, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.864.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935695
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1328, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.864.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935696
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1329, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.864.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 201935698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 1331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935700
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935702
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935703
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935706
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935710
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 201935711
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935712
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935713
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935714
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935715
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bl2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bl2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935716
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935717
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935718
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935720
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935721
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935722
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935723
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935724
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3456.oc.864.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 201935725
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': False, 'core_order': 3, 'counter': 1355, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '3456.oc.1152.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1152.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1152.157864', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8514248756003452164, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1152, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 201935726
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 1, 'counter': 1356, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1152.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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id: 201935727
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 1357, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1152.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935728
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 1358, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1152.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935729
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 1359, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1152.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1152.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1152, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
-
id: 201935731
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 1360, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935732
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': False, 'core_order': 1, 'counter': 1361, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935733
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 576, 'characteristic': False, 'core_order': 1, 'counter': 1362, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935734
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1363, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935735
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 384, 'characteristic': False, 'core_order': 1, 'counter': 1364, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935736
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1365, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935737
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 1366, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935738
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 1367, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935739
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 1368, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935740
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 1369, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935742
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 1370, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3456.oc.1728.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1728, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 201935743
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3456.oc', 'ambient_counter': 367, 'ambient_order': 3456, 'ambient_tex': 'D_6^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 3456, 'characteristic': True, 'core_order': 1, 'counter': 1371, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '3456.oc.3456.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3456.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '3456.oc', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1942231094641922994, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3456, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_6^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 201935415
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': 576, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.u1', '96.d1', '96.l1'], 'contains': ['576.d1', '576.x1', '576.bd1', '864.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [38482336575, 1970078819, 13412085120], 'label': '3456.oc.288.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.j1', 'old_label': '288.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935416
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '288.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bb1', '72.bc1', '96.n1', '144.u1'], 'contains': ['576.c1', '576.k1', '864.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1967901282, 1137042, 13412085120], 'label': '3456.oc.288.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '288.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935329
{'ambient': '3456.oc', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3456.a1', 'complements': ['3456.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '3.a1', '3.b1', '4.f1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [526, 647, 38480884412, 2588323, 2951738, 1137421, 13412085385, 1862886, 1967901282, 604203618], 'label': '3456.oc.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
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id: 201935330
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '41472.kr', 'aut_weyl_index': 1, 'centralizer': '3456.a1', 'complements': ['864.bg1', '864.e1', '864.bj1', '864.g1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.d1', '2.e1'], 'contains': ['8.a1', '12.c1', '12.bu1', '12.bv1', '16.d1', '16.h1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1967901282, 1862886, 647, 38480884412, 2588323, 526, 1137421, 604203618], 'label': '3456.oc.4.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': ['2.c1', '2.d1', '2.e1'], 'normal_contains': ['8.a1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
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id: 201935331
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.q1'], 'contains': ['24.dy1', '36.cx1', '36.cy1', '36.da1', '48.do1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 1137421, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.12.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '12.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201935332
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.bb2', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cd2', '108.p1', '108.q1', '108.r1'], 'contains': ['432.h2', '432.j2', '432.p1', '432.bn2', '432.cp2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [13413948258, 1863138, 2588323, 1967535360], 'label': '3456.oc.216.bb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.bb2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935333
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1', '72.ce1', '108.n1'], 'contains': ['432.m1', '432.n1', '432.q1', '432.di1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2587950, 13414673070, 1862886, 1969352190], 'label': '3456.oc.216.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '216.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 201935334
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ch1', '108.n1', '108.t1', '108.bf1'], 'contains': ['432.s1', '432.u1', '432.bb1', '432.bf1', '432.dc1', '432.dd1', '432.dd2', '432.dg1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085385, 526, 1862886, 1967535360], 'label': '3456.oc.216.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935335
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cf1', '72.ck1', '108.a1', '108.g1', '108.s1'], 'contains': ['432.t1', '432.v1', '432.y1', '432.bc1', '432.bd1', '432.bh1', '432.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 1862886, 2226652, 13414673322], 'label': '3456.oc.216.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '216.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935336
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ci1', '108.b1', '108.bf1'], 'contains': ['432.s1', '432.x1', '432.be3', '432.be4', '432.db1', '432.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1969352563, 13412085385, 526, 1862886], 'label': '3456.oc.216.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935337
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cg1', '72.cl1', '108.a1', '108.h1', '108.s1'], 'contains': ['432.t1', '432.y1', '432.z1', '432.bg1', '432.bi1', '432.bj1', '432.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [526, 1968991665, 1134054, 13413948127], 'label': '3456.oc.216.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935338
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cj1', '72.cm1', '108.b1', '108.k1', '108.t1'], 'contains': ['432.s1', '432.t1', '432.w1', '432.bm1', '432.bm2', '432.dd1', '432.de1', '432.df1', '432.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 13414673322], 'label': '3456.oc.216.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935339
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.cn1', '108.r1', '108.s1', '108.t1'], 'contains': ['432.t1', '432.u1', '432.bn1', '432.bn2', '432.bo1', '432.dg1', '432.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [526, 1862886, 13414673191, 1967535360], 'label': '3456.oc.216.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935340
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.co1', '72.cp1', '108.m1', '108.s1', '108.bg1'], 'contains': ['432.u1', '432.v1', '432.z1', '432.bp1', '432.bs1', '432.bx1', '432.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [265, 1862886, 2226652, 1967535360], 'label': '3456.oc.216.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935341
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.cq1', '108.m1', '108.s1', '108.bh1'], 'contains': ['432.u1', '432.y1', '432.br1', '432.bt1', '432.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [265, 13413586612, 1862886, 1967535360], 'label': '3456.oc.216.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935342
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1'], 'contains': ['24.dz1', '36.cx1', '36.cz1', '36.da1', '48.dp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37882213052, 604926858, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.12.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1', 'old_label': '12.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1', 'subgroup_fusion': None, 'weyl_group': '288.1036'}
-
id: 201935343
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.cr1', '72.cs1', '108.a1', '108.bg1'], 'contains': ['432.v1', '432.x1', '432.z1', '432.bv1', '432.bw1', '432.cd1', '432.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1969352563, 265, 1862886, 2226652], 'label': '3456.oc.216.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935344
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ct1', '108.a1', '108.bh1'], 'contains': ['432.x1', '432.y1', '432.cb1', '432.cc1', '432.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1969352563, 265, 13413586612, 1862886], 'label': '3456.oc.216.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935345
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cu1', '72.cy1', '108.a1', '108.d1', '108.u1'], 'contains': ['432.bc1', '432.be2', '432.bl1', '432.bu1', '432.bw1', '432.bz1', '432.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 1968627378], 'label': '3456.oc.216.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935346
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cv1', '72.cz1', '108.a1', '108.c1', '108.v1'], 'contains': ['432.bd1', '432.be1', '432.bj1', '432.bu1', '432.bv1', '432.ca1', '432.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13413948258, 1968627247, 1134693, 2226652], 'label': '3456.oc.216.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935347
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cw1', '72.da1', '108.a1', '108.e1', '108.u1'], 'contains': ['432.be2', '432.bg1', '432.bk1', '432.by1', '432.ca1', '432.cb1', '432.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 1968627378], 'label': '3456.oc.216.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935348
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.cx1', '72.db1', '108.a1', '108.c1', '108.w1'], 'contains': ['432.be1', '432.bh1', '432.bi1', '432.by1', '432.bz1', '432.cc1', '432.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13413948258, 1968627247, 1134693, 2951738], 'label': '3456.oc.216.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935349
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.dc1', '108.p1', '108.s1', '108.u1'], 'contains': ['432.bc1', '432.bg1', '432.bn2', '432.bp1', '432.br1', '432.dm1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2226652, 13413948127, 1967535360], 'label': '3456.oc.216.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935350
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.dd1', '108.o1', '108.s1', '108.v1'], 'contains': ['432.bd1', '432.bj1', '432.bn1', '432.bp1', '432.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 1967535360], 'label': '3456.oc.216.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935351
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.de1', '108.o1', '108.s1', '108.w1'], 'contains': ['432.bh1', '432.bi1', '432.bn1', '432.br1', '432.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 1967535360], 'label': '3456.oc.216.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935352
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.df1', '108.q1', '108.s1', '108.u1'], 'contains': ['432.bk1', '432.bl1', '432.bn2', '432.bs1', '432.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2951738, 13413948127, 1967535360], 'label': '3456.oc.216.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935353
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.d1', '48.a1', '48.c1', '48.n1', '48.o1', '64.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 2588323, 1863007, 13413948127], 'label': '3456.oc.16.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 201935354
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dg1', '72.dh1', '108.c1', '108.d1', '108.s1'], 'contains': ['432.bc1', '432.bd1', '432.bi1', '432.bl1', '432.bo1', '432.bx1', '432.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 1134693, 2226652, 13413948127], 'label': '3456.oc.216.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935355
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.di1', '72.dj1', '108.c1', '108.e1', '108.s1'], 'contains': ['432.bg1', '432.bh1', '432.bj1', '432.bk1', '432.bo1', '432.cg1', '432.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738, 13413948127], 'label': '3456.oc.216.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935356
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.dk1', '108.m1', '108.u1', '108.v1'], 'contains': ['432.bp1', '432.bq1', '432.bt1', '432.bu1', '432.ca1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 1967535360], 'label': '3456.oc.216.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935357
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.dl1', '108.m1', '108.u1', '108.w1'], 'contains': ['432.bq1', '432.br1', '432.bs1', '432.by1', '432.bz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 1967535360], 'label': '3456.oc.216.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935358
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.bz1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.dm1', '108.n1', '108.bf1'], 'contains': ['432.ba1', '432.bb1', '432.bq1', '432.ci1', '432.ck1', '432.db1', '432.dc1', '432.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323, 1967535360], 'label': '3456.oc.216.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bz1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935359
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.ca1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.dn1', '72.do1', '108.b1', '108.k1', '108.bf1'], 'contains': ['432.ba1', '432.be1', '432.be2', '432.be3', '432.be4', '432.bm1', '432.bm2', '432.ci1', '432.cj1', '432.cm1', '432.db1', '432.dd1', '432.dd2', '432.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13412085767, 1967535625, 1862886, 2588323], 'label': '3456.oc.216.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ca1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935360
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cb1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dp1', '108.r1', '108.t1', '108.bf1'], 'contains': ['432.bb1', '432.bm1', '432.bm2', '432.bn1', '432.bn2', '432.cj1', '432.ck1', '432.dc1', '432.de1', '432.dg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085385, 1862886, 2588323, 1967535360], 'label': '3456.oc.216.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935361
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cc1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dq1', '108.k1', '108.t1'], 'contains': ['432.bf1', '432.bm1', '432.bm2', '432.bo1', '432.cj1', '432.cl1', '432.dd2', '432.df1', '432.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13412085385, 1862886, 2588323], 'label': '3456.oc.216.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935362
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '216.cd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.dr1', '72.ds1', '108.b1', '108.l1', '108.t1'], 'contains': ['432.s1', '432.t1', '432.cj1', '432.cn1', '432.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 13412085385, 526, 1862886], 'label': '3456.oc.216.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935363
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.ce1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dt1', '72.du1', '108.n1', '108.t1', '108.bn1'], 'contains': ['432.u1', '432.w1', '432.ck1', '432.cl1', '432.cn1', '432.dk1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2587950, 526, 1862886, 1967535360], 'label': '3456.oc.216.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ce1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935364
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '8.e1'], 'contains': ['32.e1', '48.d1', '48.t1', '48.u1', '48.v1', '64.a1'], 'core': '192.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1137421, 2587950, 38480883894, 13414673070, 1862886, 604203366], 'label': '3456.oc.16.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '16.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '144.190'}
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id: 201935365
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.cf1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dv1', '72.dw1', '108.b1', '108.bn1'], 'contains': ['432.w1', '432.x1', '432.cm1', '432.cn1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2587950, 1967536007, 526, 1862886], 'label': '3456.oc.216.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935366
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.cg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dx1', '72.ef1', '108.c1', '108.g1', '108.u1'], 'contains': ['432.bc1', '432.bk1', '432.bu1', '432.by1', '432.co1', '432.cq1', '432.ct1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 2226652, 2588323, 1863007], 'label': '3456.oc.216.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '216.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935367
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.ch1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dy1', '72.eg1', '108.d1', '108.g1', '108.v1', '108.y1', '108.bb1'], 'contains': ['432.bd1', '432.bu1', '432.co2', '432.cr1', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 13412085385, 2226652, 1863007], 'label': '3456.oc.216.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ch1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935368
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.ci1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.ea1', '72.eh1', '108.c1', '108.h1', '108.u1'], 'contains': ['432.bg1', '432.bl1', '432.bz1', '432.ca1', '432.co1', '432.ct1', '432.cv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085646, 1968991665, 2588323, 1863007], 'label': '3456.oc.216.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ci1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935369
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.cj1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.dz1', '72.ej1', '108.e1', '108.g1', '108.w1', '108.z1', '108.bc1'], 'contains': ['432.bh1', '432.by1', '432.co2', '432.cu1', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 13412085385, 2226275, 1863007], 'label': '3456.oc.216.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935370
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.ck1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.eb1', '72.ei1', '108.d1', '108.h1', '108.w1', '108.z1', '108.bd1'], 'contains': ['432.bi1', '432.bz1', '432.co2', '432.cu1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 2588071], 'label': '3456.oc.216.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ck1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935371
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.cl1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.ec1', '72.ek1', '108.e1', '108.h1', '108.v1', '108.ba1', '108.be1'], 'contains': ['432.bj1', '432.ca1', '432.co2', '432.cw1', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 13412085385, 2588071, 1969714258], 'label': '3456.oc.216.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935372
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.cm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.ed1', '72.el1', '108.f1', '108.i1', '108.x1', '108.z1', '108.ba1', '108.bb1', '108.bc1'], 'contains': ['432.co2', '432.cx1', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2588202, 2951738, 13412085385, 1863007], 'label': '3456.oc.216.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935373
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.cn1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.ee1', '72.em1', '108.f1', '108.j1', '108.x1', '108.y1', '108.z1', '108.bd1', '108.be1'], 'contains': ['432.co2', '432.cy1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 13412085385, 2588071, 1968991665], 'label': '3456.oc.216.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cn1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935374
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.co1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.en1', '108.r1', '108.u1', '108.bf1'], 'contains': ['432.bb1', '432.be2', '432.be3', '432.bn2', '432.bq1', '432.co1', '432.cp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085385, 2588323, 1863007, 1967535360], 'label': '3456.oc.216.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935375
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1'], 'contains': ['32.a1', '32.b1', '32.c1', '32.f1', '32.g1', '48.x1', '48.ba1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1967901282, 1137042, 38480520960, 2226652, 13412085120], 'label': '3456.oc.16.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '16.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 201935376
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.co2', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.en2', '108.r1', '108.v1', '108.w1', '108.x1', '108.bf1'], 'contains': ['432.bb1', '432.be1', '432.be4', '432.bn1', '432.bq1', '432.co2', '432.cp2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085385, 1863138, 2588323, 1967535360], 'label': '3456.oc.216.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.co2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.co2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935377
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cp1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.eo1', '108.k1', '108.y1', '108.z1', '108.ba1', '108.bf1'], 'contains': ['432.ba1', '432.be3', '432.bf1', '432.bm1', '432.co2', '432.cs2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 13412085385, 1863138, 2588323], 'label': '3456.oc.216.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935378
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cp2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.eo2', '108.k1', '108.bf1'], 'contains': ['432.ba1', '432.be4', '432.bf1', '432.bm2', '432.co1', '432.cs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 13412085385, 2588323, 1863007], 'label': '3456.oc.216.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.cp2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cp2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935379
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cq1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ep1', '72.er1', '72.es1', '108.o1', '108.u1', '108.bg1'], 'contains': ['432.bp1', '432.bs1', '432.bw1', '432.cd1', '432.cp1', '432.cq1', '432.cv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.216.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935380
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cr1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.et1', '72.eu1', '108.p1', '108.v1', '108.bg1'], 'contains': ['432.bp1', '432.bv1', '432.cp2', '432.cr1', '432.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2588202, 2226652, 1863007, 1967535360], 'label': '3456.oc.216.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935381
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.cs1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.eq1', '72.ev1', '108.o1', '108.u1', '108.bh1'], 'contains': ['432.br1', '432.bt1', '432.cb1', '432.cp1', '432.ct1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413586612, 2588323, 1863007, 1967535360], 'label': '3456.oc.216.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935382
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.ct1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ew1', '108.p1', '108.w1', '108.bh1'], 'contains': ['432.br1', '432.cc1', '432.cp2', '432.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [13413586379, 2588202, 1863007, 1967535360], 'label': '3456.oc.216.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935383
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.cu1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ex1', '72.ez1', '108.q1', '108.w1', '108.x1', '108.bg1', '108.bi1'], 'contains': ['432.bs1', '432.ce1', '432.cp2', '432.cx1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 2951738, 1863007, 1967535360], 'label': '3456.oc.216.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935384
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.cv1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ey1', '108.q1', '108.v1', '108.x1', '108.bh1', '108.bj1'], 'contains': ['432.bt1', '432.cf1', '432.cp2', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 1863007, 13415398178, 1967535360], 'label': '3456.oc.216.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935385
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.cw1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fa1', '72.fb1', '108.c1', '108.bg1'], 'contains': ['432.bv1', '432.bx1', '432.ce1', '432.ch1', '432.cq1', '432.cs1', '432.cv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627126, 2226652, 2588323, 1863007], 'label': '3456.oc.216.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935386
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '8.d1', '8.f1', '8.g1'], 'contains': ['32.d1', '48.b1', '48.cy1', '48.cz1', '64.b1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1967901282, 1863007, 2586614, 604203487, 2588323, 38480884412], 'label': '3456.oc.16.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
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id: 201935387
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.cx1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fc1', '72.fd1', '108.d1', '108.y1', '108.bg1', '108.bk1'], 'contains': ['432.bw1', '432.bx1', '432.cr1', '432.cs2', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.216.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935388
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.cy1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fe1', '72.fg1', '108.d1', '108.e1', '108.z1', '108.bh1', '108.bl1'], 'contains': ['432.cb1', '432.cg1', '432.cs2', '432.cu1', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413586379, 2588202, 1967536007, 1863007], 'label': '3456.oc.216.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935389
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.cy2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ff1', '108.c1', '108.bh1'], 'contains': ['432.cc1', '432.cf1', '432.cg1', '432.cs1', '432.ct1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627126, 13413586612, 2588323, 1863007], 'label': '3456.oc.216.cy2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.cy2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cy2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935390
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.cz1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fh1', '72.fi1', '108.e1', '108.ba1', '108.bg1', '108.bm1'], 'contains': ['432.cd1', '432.ch1', '432.cs2', '432.cw1', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.216.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.cz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935391
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.da1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fj1', '72.fl1', '108.f1', '108.z1', '108.bi1', '108.bk1', '108.bm1'], 'contains': ['432.cs2', '432.cx1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2588202, 1967536007, 2226275, 1863007], 'label': '3456.oc.216.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.da1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201935392
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '216.db1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fk1', '108.f1', '108.y1', '108.ba1', '108.bj1', '108.bl1'], 'contains': ['432.cs2', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2588202, 1967536007, 1863007, 13415398178], 'label': '3456.oc.216.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.db1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935393
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '216.dc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fm1', '72.fn1', '108.k1', '108.l1', '108.bb1', '108.bc1', '108.bd1', '108.be1', '108.bf1'], 'contains': ['432.s1', '432.ci1', '432.cj1', '432.co1', '432.co2', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 526, 1862886, 2588323], 'label': '3456.oc.216.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935394
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.dd1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fo1', '72.fp1', '108.r1', '108.bf1', '108.bg1', '108.bh1', '108.bi1', '108.bj1', '108.bn1'], 'contains': ['432.u1', '432.x1', '432.ck1', '432.cm1', '432.cp1', '432.cp2', '432.cs1', '432.cs2', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [526, 1862886, 2588323, 1967535360], 'label': '3456.oc.216.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935395
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '216.de1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '24.bk1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fq1', '72.fr1', '108.g1', '108.bb1', '108.bg1', '108.bk1', '108.bo1'], 'contains': ['432.v1', '432.cq1', '432.cr1', '432.cx1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 2587950, 526, 2951391], 'label': '3456.oc.216.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.de1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935396
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.df1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fs1', '72.ft1', '108.k1', '108.bk1', '108.bl1', '108.bm1', '108.bn1'], 'contains': ['432.w1', '432.cl1', '432.cm1', '432.cs1', '432.cs2', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 2588323], 'label': '3456.oc.216.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.df1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935397
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 216, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '8.b1', '8.f1'], 'contains': ['32.d1', '48.db1', '48.dd1', '48.de1', '64.c1'], 'core': '96.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.16.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 201935398
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.dg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fu1', '72.fv1', '108.g1', '108.h1', '108.bc1', '108.bd1', '108.bh1', '108.bl1', '108.bp1'], 'contains': ['432.y1', '432.ct1', '432.cu1', '432.cy1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 526, 13415398178], 'label': '3456.oc.216.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935399
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.dh1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fw1', '72.fx1', '108.h1', '108.be1', '108.bg1', '108.bm1', '108.bq1'], 'contains': ['432.z1', '432.cv1', '432.cw1', '432.cz1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 526, 1968991665, 2588323], 'label': '3456.oc.216.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935400
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '216.di1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '24.bk1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.fy1', '72.gc1', '108.i1', '108.bc1', '108.bi1', '108.bm1', '108.bo1'], 'contains': ['432.cx1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 526], 'label': '3456.oc.216.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.di1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935401
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '216.dj1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.fz1', '72.ga1', '108.i1', '108.j1', '108.bb1', '108.be1', '108.bj1', '108.bl1', '108.bp1'], 'contains': ['432.cy1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 526, 13415397945], 'label': '3456.oc.216.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935402
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.dk1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.gb1', '72.gd1', '108.j1', '108.bd1', '108.bi1', '108.bk1', '108.bq1'], 'contains': ['432.cz1', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 1968991316, 526, 2588323], 'label': '3456.oc.216.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935403
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.dl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gh1', '108.n1', '108.t1'], 'contains': ['432.dc1', '432.df1', '432.dg1', '432.dj1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2587950, 13412085385, 1862886, 1969352190], 'label': '3456.oc.216.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935404
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.dm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gi1', '108.b1', '108.t1'], 'contains': ['432.dd2', '432.de1', '432.dh1', '432.dj1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2587950, 1967536007, 13412085385, 1862886], 'label': '3456.oc.216.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.dm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935405
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.a1', 'aut_quo_index': 4, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '12.b1', 'complements': ['12.s1'], 'conjugacy_class_count': 6, 'contained_in': ['96.b1', '96.bd1', '96.be1', '144.a1', '144.k1', '144.ex1', '144.ey1', '144.fa1', '144.fc1', '144.fh1', '144.fj1', '144.fl1', '144.fp1', '144.gc1'], 'contains': ['576.e1', '864.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480884412, 2588323, 1863007], 'label': '3456.oc.288.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.a1', 'normal_contained_in': ['72.a1', '96.b1', '144.a1'], 'normal_contains': ['864.a1', '1152.a1'], 'normalizer': '1.a1', 'old_label': '288.a1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '24.15', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '288.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935406
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.e1', '144.b1', '144.c1', '144.d1', '144.e1', '144.f1', '144.g1', '144.h1', '144.i1', '144.i2', '144.j1', '144.k1', '144.k2', '144.bk1'], 'contains': ['576.b1', '576.e1', '576.i1', '864.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 38480884533, 13412085120], 'label': '3456.oc.288.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935407
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '144.b1', '144.j1', '144.n1', '144.o1', '144.p1', '144.q1', '144.bl1'], 'contains': ['576.b1', '576.g1', '576.q1', '864.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 13412085120], 'label': '3456.oc.288.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935408
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.d1', '8.b1', '8.c1', '8.g1'], 'contains': ['32.d1', '48.dg1', '48.dh1', '48.di1', '48.dk1', '64.d1'], 'core': '96.b1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1137300, 604203487, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.16.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 201935409
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.g1', '144.h1', '144.i1', '144.i2', '144.n1', '144.o1', '144.t1', '144.bk1'], 'contains': ['576.b1', '576.j1', '576.s1', '864.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627499, 38480520960, 13412085120], 'label': '3456.oc.288.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935410
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.c1', '96.h1', '144.c1', '144.t1', '144.bm1'], 'contains': ['576.b1', '576.n1', '576.u1', '864.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38480520960, 2226652, 13412085120], 'label': '3456.oc.288.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935411
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.r1', '96.c1', '96.i1', '144.u1'], 'contains': ['576.c1', '576.p1', '576.w1', '864.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137042, 2226652, 13412085120], 'label': '3456.oc.288.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '288.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935412
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.j1', '144.d1', '144.h1', '144.n1', '144.p1', '144.bl1'], 'contains': ['576.b1', '576.r1', '576.y1', '864.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 38480520960, 13412085120], 'label': '3456.oc.288.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935413
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.d1', '96.m1', '144.e1', '144.t1', '144.bm1'], 'contains': ['576.b1', '576.v1', '576.ba1', '864.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38480520960, 1970078819, 13412085120], 'label': '3456.oc.288.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935414
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.t1', '96.d1', '96.k1', '144.u1'], 'contains': ['576.c1', '576.w1', '576.bc1', '864.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 288, 'diagramx': None, 'generators': [1137042, 1970078819, 13412085120], 'label': '3456.oc.288.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '288.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935417
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.e1', '144.a1', '144.v1', '144.w1', '144.x1', '144.y1', '144.z1', '144.ba1', '144.bb1', '144.bc1', '144.bc2', '144.bd1', '144.be1', '144.bk1'], 'contains': ['576.a1', '576.e1', '576.j1', '864.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 39798138933, 13412085120], 'label': '3456.oc.288.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935418
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '144.v1', '144.bd1', '144.bf1', '144.bg1', '144.bh1', '144.bi1', '144.bl1'], 'contains': ['576.a1', '576.g1', '576.r1', '864.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39797775360, 1862886, 13412085120], 'label': '3456.oc.288.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935419
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.e1', '8.c1', '8.f1'], 'contains': ['32.d1', '48.dl1', '48.dm1', '48.dn1', '48.do1', '48.dp1', '64.e1'], 'core': '96.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.16.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201935420
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.g1', '144.bb1', '144.bc1', '144.bc2', '144.bf1', '144.bg1', '144.bj1', '144.bk1'], 'contains': ['576.a1', '576.i1', '576.s1', '864.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627499, 13413948379, 38480520960], 'label': '3456.oc.288.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935421
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.h1', '96.i1', '144.w1', '144.bj1', '144.bm1'], 'contains': ['576.a1', '576.n1', '576.v1', '864.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39797775360, 2226652, 13412085120], 'label': '3456.oc.288.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '288.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935422
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.j1', '144.x1', '144.bb1', '144.bf1', '144.bh1', '144.bl1'], 'contains': ['576.a1', '576.q1', '576.y1', '864.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1967536007, 38480520960], 'label': '3456.oc.288.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935423
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.k1', '96.l1', '96.m1', '144.y1', '144.bj1', '144.bm1'], 'contains': ['576.a1', '576.u1', '576.ba1', '864.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39797775360, 1970078819, 13412085120], 'label': '3456.oc.288.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935424
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.a1', '96.n1', '144.bk1', '144.bl1', '144.bm1'], 'contains': ['576.a1', '576.b1', '576.l1', '864.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480520960, 1967535360, 13412085120], 'label': '3456.oc.288.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '288.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935425
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.o1', '144.b1', '144.v1', '144.bn1', '144.bo1', '144.bp1', '144.bq1', '144.br1', '144.bt1', '144.bv1', '144.bx1', '144.bz1', '144.ca1', '144.cb1', '144.ev1', '144.gc1'], 'contains': ['576.e1', '576.g1', '864.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [526, 1862886, 38481612978], 'label': '3456.oc.288.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935426
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.o1', '144.bs1', '144.bu1', '144.bw1', '144.by1', '144.cc1', '144.ew1', '144.gd1'], 'contains': ['576.f1', '576.h1', '864.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37882941618, 526, 1862886], 'label': '3456.oc.288.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '288.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935427
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.u1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.p1', '144.j1', '144.bb1', '144.bn1', '144.cd1', '144.co1', '144.cp1', '144.cp2', '144.cq1', '144.db1', '144.db2', '144.el1', '144.em1', '144.ex1', '144.ex2'], 'contains': ['576.e1', '576.i1', '576.q1', '864.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 13412085385, 38480884533], 'label': '3456.oc.288.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935428
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.v1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.q1', '144.k1', '144.bc1', '144.bo1', '144.cf1', '144.cg1', '144.ch1', '144.cj1', '144.ck1', '144.cr1', '144.dc1', '144.dd1', '144.em1', '144.ex2'], 'contains': ['576.e1', '576.i1', '864.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1134693, 38480884533], 'label': '3456.oc.288.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935429
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.v2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.q2', '144.k2', '144.bc2', '144.bo1', '144.ce1', '144.cg2', '144.ci1', '144.cl1', '144.cm1', '144.cr2', '144.dc2', '144.dd2', '144.em1', '144.ex1'], 'contains': ['576.e1', '576.i1', '864.k2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 13413948127, 38480884533], 'label': '3456.oc.288.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.v2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.v2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935430
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '8.e1'], 'contains': ['32.e1', '48.ee1', '48.ef1', '48.eg1', '64.b1'], 'core': '192.b1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [2587950, 38480883894, 1967901282, 1862886, 1137042, 604203366], 'label': '3456.oc.16.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '16.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
-
id: 201935431
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.w1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.p1', '144.h1', '144.bd1', '144.bp1', '144.cn1', '144.co1', '144.cp1', '144.cp2', '144.cq1', '144.cr1', '144.cr2', '144.en1', '144.eo1', '144.ey1', '144.ey2'], 'contains': ['576.e1', '576.j1', '576.r1', '864.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1134693, 13412085385, 39798138933], 'label': '3456.oc.288.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935432
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.q1', '144.a1', '144.i1', '144.bq1', '144.ct1', '144.cu1', '144.cw1', '144.cx1', '144.cy1', '144.db1', '144.dc1', '144.dd2', '144.eo1', '144.ey2'], 'contains': ['576.e1', '576.j1', '864.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 1134693, 39798138933], 'label': '3456.oc.288.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935433
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.x2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.q2', '144.i2', '144.be1', '144.bq1', '144.cs1', '144.cu2', '144.cv1', '144.cz1', '144.da1', '144.db2', '144.dc2', '144.dd1', '144.eo1', '144.ey1'], 'contains': ['576.e1', '576.j1', '864.k2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 39798138933, 13413948127], 'label': '3456.oc.288.x2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.x2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.x2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935434
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '288.y1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.r1', '144.bk1', '144.br1', '144.co1', '144.dc1', '144.dc2', '144.de1', '144.dg1', '144.dh1', '144.di1', '144.dj1', '144.ep1', '144.fa1', '144.fa2'], 'contains': ['576.e1', '576.l1', '576.s1', '864.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 1967535360, 38480884533], 'label': '3456.oc.288.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935435
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '288.z1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.r1', '144.bs1', '144.df1', '144.dk1', '144.eq1', '144.fb1', '144.fb2'], 'contains': ['576.f1', '576.m1', '576.t1', '864.l1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 37882213173, 1967535360], 'label': '3456.oc.288.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '288.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935436
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.t1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.s1', '144.c1', '144.w1', '144.bt1', '144.ce1', '144.cf1', '144.cs1', '144.ct1', '144.de1', '144.dl1', '144.dm1', '144.dn1', '144.dp1', '144.dr1', '144.fc1', '144.fe1'], 'contains': ['576.e1', '576.n1', '864.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2226652, 38480884533], 'label': '3456.oc.288.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '288.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935437
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.s1', '144.bu1', '144.df1', '144.do1', '144.dq1', '144.ds1', '144.fd1', '144.ff1'], 'contains': ['576.f1', '576.o1', '864.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 37882213173, 2226652], 'label': '3456.oc.288.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935438
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.bc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.t1', '144.b1', '144.x1', '144.cn1', '144.cu1', '144.cu2', '144.dg1', '144.dl1', '144.dt1', '144.du1', '144.dv1', '144.el1', '144.ex1', '144.ex2'], 'contains': ['576.e1', '576.q1', '864.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1134693, 38480884533], 'label': '3456.oc.288.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935439
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.t1', '144.d1', '144.v1', '144.cd1', '144.cg1', '144.cg2', '144.dg1', '144.dm1', '144.dw1', '144.dx1', '144.dy1', '144.en1', '144.ey1', '144.ey2'], 'contains': ['576.e1', '576.r1', '864.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 1134693, 39798138933], 'label': '3456.oc.288.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935440
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.be1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.u1', '144.h1', '144.bb1', '144.bv1', '144.cd1', '144.cn1', '144.cr1', '144.cr2', '144.db1', '144.db2', '144.ep1', '144.er1', '144.et1', '144.fh1', '144.fh2'], 'contains': ['576.e1', '576.s1', '576.y1', '864.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 38480884533], 'label': '3456.oc.288.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935441
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '4608.dp', 'aut_weyl_index': 9, 'centralizer': '384.a1', 'complements': ['864.h1', '864.d1', '864.bk1', '864.bl2', '864.bo1', '864.f1', '864.bs1', '864.bh1', '864.br1', '864.bi1', '864.bm1', '864.bl1', '864.g1', '864.bj1', '864.bp1', '864.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '12.d1', '12.bw1', '12.bx1', '16.e1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1137421, 2951738, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.4.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '12.d1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
-
id: 201935442
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '9.b1'], 'contains': ['36.f1', '36.h1', '36.i1', '36.l1', '36.m1', '36.bo1', '36.bp1', '36.bw1', '36.bx1', '36.ch1', '36.cj1', '54.a1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 13413948127, 2951391], 'label': '3456.oc.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935443
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.bf1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.u1', '144.bw1', '144.eq1', '144.es1', '144.eu1', '144.fi1', '144.fi2'], 'contains': ['576.f1', '576.t1', '576.z1', '864.o1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 37882213173], 'label': '3456.oc.288.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '288.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935444
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.v1', '144.i1', '144.bc1', '144.bx1', '144.cg2', '144.cp1', '144.cu2', '144.dp1', '144.dz1', '144.ea1', '144.ec1', '144.et1', '144.fa1', '144.fh2'], 'contains': ['576.e1', '576.s1', '864.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 1968627378, 38480884533], 'label': '3456.oc.288.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935445
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bg2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.v2', '144.i2', '144.bc2', '144.bx1', '144.cg1', '144.cp2', '144.cu1', '144.dn1', '144.eb1', '144.ee1', '144.ef1', '144.et1', '144.fa2', '144.fh1'], 'contains': ['576.e1', '576.s1', '864.p2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627247, 1134693, 38480884533], 'label': '3456.oc.288.bg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.bg2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bg2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935446
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bh1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.v1', '144.by1', '144.dq1', '144.ed1', '144.eu1', '144.fb1', '144.fi2'], 'contains': ['576.f1', '576.t1', '864.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 37882213173, 1968627378], 'label': '3456.oc.288.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '288.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935447
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bh2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.v2', '144.by1', '144.do1', '144.eg1', '144.eu1', '144.fb2', '144.fi1'], 'contains': ['576.f1', '576.t1', '864.p2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627247, 1134693, 37882213173], 'label': '3456.oc.288.bh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '288.bh2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bh2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935448
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.bi1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.w1', '144.c1', '144.y1', '144.bz1', '144.ce1', '144.ch1', '144.cv1', '144.cw1', '144.dh1', '144.dt1', '144.dw1', '144.dz1', '144.eb1', '144.eh1', '144.fj1', '144.fk1'], 'contains': ['576.e1', '576.u1', '864.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 13414311772, 38480884533], 'label': '3456.oc.288.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '288.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935449
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.w1', '144.e1', '144.w1', '144.ca1', '144.ci1', '144.cj1', '144.cs1', '144.cx1', '144.dh1', '144.du1', '144.dx1', '144.ea1', '144.eb1', '144.ei1', '144.fl1', '144.fo1'], 'contains': ['576.e1', '576.v1', '864.q1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 13414311772, 39798138933], 'label': '3456.oc.288.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '288.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935450
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bk1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.x1', '144.d1', '144.x1', '144.br1', '144.cq1', '144.dd1', '144.dd2', '144.dr1', '144.eh1', '144.ei1', '144.ej1', '144.er1', '144.fh1', '144.fh2'], 'contains': ['576.e1', '576.y1', '864.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 1134693, 38480884533], 'label': '3456.oc.288.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935451
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.bl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.x1', '144.bs1', '144.ds1', '144.ek1', '144.es1', '144.fi1', '144.fi2'], 'contains': ['576.f1', '576.z1', '864.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 1134693, 37882213173], 'label': '3456.oc.288.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '288.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935452
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.bm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.y1', '144.e1', '144.y1', '144.cb1', '144.ci1', '144.ck1', '144.cv1', '144.cy1', '144.de1', '144.dn1', '144.dv1', '144.dy1', '144.ec1', '144.ej1', '144.fp1', '144.fu1'], 'contains': ['576.e1', '576.ba1', '864.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078819, 38481613099], 'label': '3456.oc.288.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '288.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935453
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '9.b1'], 'contains': ['36.g1', '36.h1', '36.j1', '36.k1', '36.m1', '36.bq1', '36.br1', '36.by1', '36.bz1', '36.ck1', '36.cl1', '54.b1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 2951738, 526, 13413948127], 'label': '3456.oc.18.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935454
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.bn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.y1', '144.cc1', '144.df1', '144.do1', '144.ed1', '144.ek1', '144.fq1', '144.fv1'], 'contains': ['576.f1', '576.bb1', '864.s1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 37882941739, 1970078819], 'label': '3456.oc.288.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '288.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935455
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.bo1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.z1', '144.f1', '144.z1', '144.bt1', '144.ch1', '144.cl1', '144.cx1', '144.cz1', '144.di1', '144.dt1', '144.dx1', '144.ec1', '144.ee1', '144.ej1', '144.fc1', '144.fw1'], 'contains': ['576.e1', '864.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2951738, 38480884533], 'label': '3456.oc.288.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '288.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935456
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.bp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ba1', '144.f1', '144.ba1', '144.bz1', '144.cf1', '144.cl1', '144.cy1', '144.da1', '144.dj1', '144.dl1', '144.dy1', '144.ea1', '144.ef1', '144.ei1', '144.fj1', '144.fx1'], 'contains': ['576.e1', '864.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13415036858, 1134693, 38480884533], 'label': '3456.oc.288.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '288.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bp1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935457
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.bu1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ba1', '144.g1', '144.z1', '144.ca1', '144.ck1', '144.cm1', '144.ct1', '144.cz1', '144.dj1', '144.dm1', '144.dv1', '144.dz1', '144.ef1', '144.eh1', '144.fl1', '144.fy1'], 'contains': ['576.e1', '864.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13415036858, 1134693, 39798138933], 'label': '3456.oc.288.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '288.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201935458
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.br1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bb1', '144.g1', '144.ba1', '144.cb1', '144.cj1', '144.cm1', '144.cw1', '144.da1', '144.di1', '144.dp1', '144.dr1', '144.du1', '144.dw1', '144.ee1', '144.fp1', '144.fz1'], 'contains': ['576.e1', '864.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 38481613099], 'label': '3456.oc.288.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '288.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201935459
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.bs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '48.dr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.z1', '144.bu1', '144.dk1', '144.ed1', '144.eg1', '144.ek1', '144.fd1', '144.ga1'], 'contains': ['576.f1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2951738, 37882213173], 'label': '3456.oc.288.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '288.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bs1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935460
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.bt1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bb1', '144.cc1', '144.dk1', '144.dq1', '144.ds1', '144.eg1', '144.fq1', '144.gb1'], 'contains': ['576.f1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 37882941739], 'label': '3456.oc.288.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '288.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bt1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935461
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.bu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bc1', '144.j1', '144.bd1', '144.el1', '144.em1', '144.en1', '144.eo1', '144.ep1', '144.er1', '144.et1', '144.ev1', '144.gc1'], 'contains': ['576.e1', '576.g1', '864.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1862886, 2588323, 38480884533], 'label': '3456.oc.288.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935462
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.bv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bc1', '144.eq1', '144.es1', '144.eu1', '144.ew1', '144.gd1'], 'contains': ['576.f1', '576.h1', '864.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1862886, 37882213173, 2588323], 'label': '3456.oc.288.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '288.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935463
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bf1', '144.k2', '144.be1', '144.ex2', '144.ey2', '144.fa2', '144.fe1', '144.fh2', '144.fk1', '144.fo1', '144.fu1', '144.fw1', '144.fx1', '144.fy1', '144.fz1', '144.gc1'], 'contains': ['576.e1', '864.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480884129, 1863138, 2588323], 'label': '3456.oc.288.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '288.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935464
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1', '6.g1', '9.b1'], 'contains': ['36.i1', '36.k1', '36.n1', '36.bs1', '36.bt1', '36.cq1', '36.cs1', '54.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085385, 1862886, 2951738, 647, 38480884412, 2588323, 526], 'label': '3456.oc.18.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935465
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.b1', '96.bg1', '96.bh1', '144.fb1', '144.fd1', '144.fi1', '144.fq1', '144.gd1'], 'contains': ['576.f1', '864.a1'], 'core': '864.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 2588323, 1863007], 'label': '3456.oc.288.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '288.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935466
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '288.bx2', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '12.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bf1', '144.fb2', '144.ff1', '144.fi2', '144.fv1', '144.ga1', '144.gb1', '144.gd1'], 'contains': ['576.f1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1863138, 37882212769, 2588323], 'label': '3456.oc.288.bx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '288.bx2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bx2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935467
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '288.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.b1', '96.bd1', '96.bg1', '144.l1', '144.ez1', '144.fg1', '144.fm1', '144.fr1'], 'contains': ['864.a1', '1152.c1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1137421, 2588323, 1863007], 'label': '3456.oc.288.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '288.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.by1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201935468
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '288.bz1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.gf1', '96.bd1', '96.be1', '96.bh1', '144.m1', '144.fn1', '144.fs1'], 'contains': ['864.a1', '1152.d1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [38482336681, 2588323, 1863007], 'label': '3456.oc.288.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '288.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.bz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201935469
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '288.ca1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.gg1', '96.be1', '96.bg1', '96.bh1', '144.ft1'], 'contains': ['864.a1', '1152.e1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [37883665321, 2588323, 1863007], 'label': '3456.oc.288.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '288.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ca1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201935470
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.cb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bi1', '144.b1', '144.bf1', '144.bn1', '144.el1', '144.em1', '144.ge1', '144.gh1', '144.gi1', '144.gm1', '144.gn1', '144.gr1'], 'contains': ['576.g1', '576.i1', '576.q1', '864.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 13412085385, 1862886], 'label': '3456.oc.288.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935471
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.cc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bj1', '144.j1', '144.bg1', '144.bn1', '144.bo1', '144.em1', '144.gf1', '144.gj1', '144.gk1', '144.go1', '144.gp1', '144.gr1'], 'contains': ['576.g1', '576.i1', '864.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 13414673322], 'label': '3456.oc.288.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935472
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.cd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bi1', '144.n1', '144.v1', '144.bp1', '144.en1', '144.eo1', '144.gg1', '144.gh1', '144.gi1', '144.gj1', '144.gk1', '144.gs1'], 'contains': ['576.g1', '576.j1', '576.r1', '864.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085385, 39797775360, 1862886], 'label': '3456.oc.288.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935473
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bj1', '144.o1', '144.bd1', '144.bp1', '144.bq1', '144.eo1', '144.gl1', '144.gm1', '144.gn1', '144.go1', '144.gp1', '144.gs1'], 'contains': ['576.g1', '576.j1', '864.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39797775360, 1862886, 13414673322], 'label': '3456.oc.288.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ce1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935474
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.cf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bk1', '144.bl1', '144.br1', '144.ep1', '144.gh1', '144.go1', '144.gq1', '144.gu1'], 'contains': ['576.g1', '576.l1', '576.y1', '864.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 1967535360], 'label': '3456.oc.288.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935475
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.c1', '9.a1'], 'contains': ['36.b1', '36.o1', '36.cu1', '54.c1', '72.r1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 2951738, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935476
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.cg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bk1', '144.bs1', '144.eq1', '144.gv1'], 'contains': ['576.h1', '576.m1', '576.z1', '864.ba1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882941366, 1862886, 1967535360], 'label': '3456.oc.288.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '288.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935477
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.ch1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bl1', '144.q1', '144.bh1', '144.bn1', '144.el1', '144.gg1', '144.gl1', '144.gq1'], 'contains': ['576.g1', '576.q1', '864.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886], 'label': '3456.oc.288.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ch1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935478
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '288.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bl1', '144.p1', '144.bi1', '144.bp1', '144.en1', '144.ge1', '144.gf1', '144.gq1'], 'contains': ['576.g1', '576.r1', '864.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13414673070, 39797775360, 1862886], 'label': '3456.oc.288.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '288.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935479
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.cj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bm1', '144.n1', '144.bf1', '144.br1', '144.bv1', '144.er1', '144.et1', '144.gf1', '144.gi1', '144.gl1', '144.gp1', '144.gw1'], 'contains': ['576.g1', '576.s1', '576.y1', '864.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 38481612726, 1862886], 'label': '3456.oc.288.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935480
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.ck1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bm1', '144.bs1', '144.bw1', '144.es1', '144.eu1', '144.gx1'], 'contains': ['576.h1', '576.t1', '576.z1', '864.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882941366, 1967536007, 1862886], 'label': '3456.oc.288.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '288.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ck1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935481
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.cl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bn1', '144.o1', '144.bg1', '144.bv1', '144.bx1', '144.ep1', '144.et1', '144.ge1', '144.gg1', '144.gj1', '144.gm1', '144.gw1'], 'contains': ['576.g1', '576.s1', '864.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352442], 'label': '3456.oc.288.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935482
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.cm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.bn1', '144.bw1', '144.by1', '144.eq1', '144.eu1', '144.gx1'], 'contains': ['576.h1', '576.t1', '864.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882941366, 1862886, 1969352442], 'label': '3456.oc.288.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '288.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935483
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.cn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bo1', '144.p1', '144.bh1', '144.bv1', '144.er1', '144.gk1', '144.gn1', '144.gu1'], 'contains': ['576.g1', '576.y1', '864.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352190], 'label': '3456.oc.288.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935484
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.co1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bo1', '144.bw1', '144.es1', '144.gv1'], 'contains': ['576.h1', '576.z1', '864.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882941366, 1862886, 1969352190], 'label': '3456.oc.288.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '288.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935485
{'ambient': '3456.oc', 'aut_centralizer_order': 864, 'aut_label': '288.cp1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bp1', '96.bq1', '96.br1', '144.q1', '144.bi1', '144.ev1', '144.gr1', '144.gs1', '144.gu1', '144.gw1'], 'contains': ['576.g1', '864.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886], 'label': '3456.oc.288.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '288.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cp1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 201935486
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.j1', '9.b1'], 'contains': ['36.j1', '36.l1', '36.n1', '36.bu1', '36.bv1', '36.ct1', '36.cw1', '54.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085385, 38480884412, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.18.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935487
{'ambient': '3456.oc', 'aut_centralizer_order': 864, 'aut_label': '288.cq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.br1', '96.bs1', '96.bt1', '144.ew1', '144.gv1', '144.gx1'], 'contains': ['576.h1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [37882212534, 2587950, 1862886], 'label': '3456.oc.288.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '288.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cq1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 201935488
{'ambient': '3456.oc', 'aut_centralizer_order': 216, 'aut_label': '288.cr1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '96.bp1', '96.bs1', '144.r1', '144.gt1'], 'contains': ['864.bf1', '1152.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [1137421, 2587950, 1862886], 'label': '3456.oc.288.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '288.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cr1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201935489
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '288.cs1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.gf1', '96.bp1', '96.bq1', '96.bt1', '144.s1'], 'contains': ['864.bf1', '1152.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [2587950, 38482336681, 1862886], 'label': '3456.oc.288.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '288.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cs1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201935490
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '288.ct1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.gg1', '96.bq1', '96.bs1', '96.bt1'], 'contains': ['864.bf1', '1152.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [37883665321, 2587950, 1862886], 'label': '3456.oc.288.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '288.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.ct1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201935491
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.cu1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bu1', '144.c1', '144.bj1', '144.ce1', '144.gy1', '144.gz1'], 'contains': ['576.i1', '576.n1', '576.u1', '864.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [38480520960, 2226652, 13413948127], 'label': '3456.oc.288.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cu1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935492
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.cv1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bv1', '144.h1', '144.bg1', '144.cd1', '144.cg1', '144.cg2', '144.co1', '144.cp1', '144.cp2', '144.cr1', '144.cr2', '144.ge1', '144.gf1', '144.gi1', '144.gj1'], 'contains': ['576.i1', '576.r1', '576.s1', '864.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13413948258, 1968627499, 38480520960], 'label': '3456.oc.288.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935493
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.cw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bw1', '144.d1', '144.bf1', '144.cd1', '144.cq1', '144.cr1', '144.cr2', '144.gf1', '144.gh1', '144.gk1'], 'contains': ['576.i1', '576.r1', '576.y1', '864.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 13413948379, 38480520960], 'label': '3456.oc.288.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935494
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.cx1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bx1', '144.e1', '144.bj1', '144.ci1', '144.gy1', '144.gz1'], 'contains': ['576.i1', '576.v1', '576.ba1', '864.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [38480520960, 1970078819, 13413219692], 'label': '3456.oc.288.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935495
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.cy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bu1', '144.t1', '144.w1', '144.cs1', '144.gy1', '144.gz1'], 'contains': ['576.j1', '576.n1', '576.v1', '864.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39797775360, 2226652, 13413948127], 'label': '3456.oc.288.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '288.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935496
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.cz1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bv1', '144.o1', '144.bb1', '144.cn1', '144.co1', '144.cp1', '144.cp2', '144.cu1', '144.cu2', '144.db1', '144.db2', '144.gg1', '144.gi1', '144.gl1', '144.gm1'], 'contains': ['576.j1', '576.q1', '576.s1', '864.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1968627499, 38480520960], 'label': '3456.oc.288.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.cz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935497
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.h1', '9.a1'], 'contains': ['36.o1', '36.cu1', '36.cy1', '54.d1', '72.t1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1137421, 13412085385, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.18.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935498
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.da1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bw1', '144.n1', '144.x1', '144.cn1', '144.cq1', '144.db1', '144.db2', '144.gh1', '144.gl1', '144.gn1'], 'contains': ['576.j1', '576.q1', '576.y1', '864.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 13414673070, 38480520960], 'label': '3456.oc.288.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.da1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935499
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.db1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bx1', '144.t1', '144.y1', '144.cv1', '144.gy1', '144.gz1'], 'contains': ['576.j1', '576.u1', '576.ba1', '864.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [39797775360, 1970078819, 13413219692], 'label': '3456.oc.288.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.db1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935500
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '288.dc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.by1', '144.bk1', '144.co1', '144.dc1', '144.dc2', '144.gh1', '144.go1', '144.gy1'], 'contains': ['576.i1', '576.j1', '576.l1', '864.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 38480520960, 1967535360], 'label': '3456.oc.288.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935501
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.dd1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.bz1', '144.i1', '144.bc1', '144.cp2', '144.cr2', '144.db2', '144.dc1', '144.gj1', '144.gm1', '144.gp1'], 'contains': ['576.i1', '576.j1', '576.s1', '864.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413219409, 1968627499, 38480520960], 'label': '3456.oc.288.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935502
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.dd2', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.bz2', '144.i2', '144.bc2', '144.cp1', '144.cr1', '144.db1', '144.dc2', '144.gj1', '144.gm1', '144.gp1', '144.gz1'], 'contains': ['576.i1', '576.j1', '576.s1', '864.bl2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627499, 13414673191, 38480520960], 'label': '3456.oc.288.dd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '288.dd2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dd2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935503
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.de1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['96.ca1', '144.h1', '144.bb1', '144.cq1', '144.cr1', '144.cr2', '144.db1', '144.db2', '144.dd1', '144.dd2', '144.gi1', '144.gk1', '144.gn1', '144.go1', '144.gp1'], 'contains': ['576.i1', '576.j1', '576.y1', '864.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967536007, 38480520960, 13413948127], 'label': '3456.oc.288.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.de1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935504
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '288.df1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ep1', '96.cb1', '96.cc1', '144.u1'], 'contains': ['576.k1', '576.p1', '576.bc1', '864.bn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1967901282, 1137042, 2226652], 'label': '3456.oc.288.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '288.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.df1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935505
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '288.dg1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.eq1', '96.cd1', '144.u1'], 'contains': ['576.k1', '576.w1', '864.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1967901282, 13414311772, 1137042], 'label': '3456.oc.288.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '288.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935506
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.dh1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.cb1', '96.ce1', '144.bm1', '144.de1', '144.gy1'], 'contains': ['576.l1', '576.n1', '576.ba1', '864.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38480520960, 2226652, 1967535360], 'label': '3456.oc.288.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935507
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.di1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.cc1', '96.ce1', '144.df1'], 'contains': ['576.m1', '576.o1', '576.bb1', '864.bn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [37881446400, 2226652, 1967535360], 'label': '3456.oc.288.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.eu1', 'old_label': '288.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.di1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935508
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.d1', '6.i1'], 'contains': ['36.p1', '36.cv1', '36.cz1', '54.d1', '72.u1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38482336681, 13412085385, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.18.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '18.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935509
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '288.dj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.cf1', '144.bl1', '144.co1', '144.dg1', '144.gh1', '144.gq1'], 'contains': ['576.l1', '576.q1', '576.r1', '864.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 38480520960, 1967535360], 'label': '3456.oc.288.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935510
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.dk1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.cd1', '96.cg1', '144.bm1', '144.dh1', '144.gy1'], 'contains': ['576.l1', '576.u1', '576.v1', '864.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13414311772, 38480520960, 1967535360], 'label': '3456.oc.288.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935511
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.dl1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ch1', '144.t1', '144.bj1', '144.de1', '144.dn1', '144.gz1'], 'contains': ['576.n1', '576.s1', '576.ba1', '864.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 38480520960, 2226652], 'label': '3456.oc.288.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935512
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.dm1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.ch1', '144.df1', '144.do1'], 'contains': ['576.o1', '576.t1', '576.bb1', '864.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 37881446400, 2226652], 'label': '3456.oc.288.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.eu1', 'old_label': '288.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935513
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '288.dn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ci1', '144.n1', '144.bf1', '144.cd1', '144.cn1', '144.cp1', '144.cp2', '144.dg1', '144.ge1', '144.gg1'], 'contains': ['576.q1', '576.r1', '576.s1', '864.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627499, 38480520960, 13413948006], 'label': '3456.oc.288.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935514
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '288.do1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['96.cj1', '144.p1', '144.bh1', '144.cd1', '144.cn1', '144.cq1', '144.gi1', '144.gq1'], 'contains': ['576.q1', '576.r1', '576.y1', '864.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967536007, 13412085385, 38480520960], 'label': '3456.oc.288.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '288.do1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935515
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '288.dp1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.ck1', '144.t1', '144.bj1', '144.dh1', '144.eb1', '144.gz1'], 'contains': ['576.s1', '576.u1', '576.v1', '864.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 13414311772, 38480520960], 'label': '3456.oc.288.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '288.dp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935516
{'ambient': '3456.oc', 'aut_centralizer_order': 5184, 'aut_label': '384.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '4.c1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '192.a1', '192.b1', '192.f1', '192.g1', '192.h1', '192.k1', '192.n1', '192.o1', '192.r1', '192.t1', '192.w1'], 'contains': ['1152.a1', '1152.b1'], 'core': '384.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [602743680, 38480520960], 'label': '3456.oc.384.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '384.a1', 'normal_contained_in': ['96.b1', '192.a1', '192.b1'], 'normal_contains': ['1152.a1'], 'normalizer': '1.a1', 'old_label': '384.a1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '96.227', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '384.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935517
{'ambient': '3456.oc', 'aut_centralizer_order': 324, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.bd1', '96.bp1', '128.a1', '192.c1', '192.d1', '192.i1', '192.l1', '192.p1', '192.s1', '192.u1'], 'contains': ['1152.a1', '1152.c1', '1152.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1137421, 38480520960], 'label': '3456.oc.384.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '384.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935518
{'ambient': '3456.oc', 'aut_centralizer_order': 162, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.be1', '96.bq1', '128.a1', '192.e1', '192.q1', '192.v1'], 'contains': ['1152.a1', '1152.d1', '1152.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [604926858, 38480520960], 'label': '3456.oc.384.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1', 'old_label': '384.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935519
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1', '9.a1'], 'contains': ['36.o1', '36.cn1', '54.g1', '72.bb1', '72.bc1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1137421, 13412085385, 1967901282, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935520
{'ambient': '3456.oc', 'aut_centralizer_order': 324, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bg1', '96.bs1', '128.a1', '192.j1', '192.m1', '192.x1'], 'contains': ['1152.b1', '1152.c1', '1152.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1137421, 37881446400], 'label': '3456.oc.384.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '384.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935521
{'ambient': '3456.oc', 'aut_centralizer_order': 162, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.bh1', '96.bt1', '128.a1', '192.y1'], 'contains': ['1152.b1', '1152.d1', '1152.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [37881446400, 604926858], 'label': '3456.oc.384.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.e1', 'old_label': '384.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935522
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.b1', '144.v1', '216.b1', '216.c1', '216.d1', '216.e1', '216.n1', '216.v1', '216.x1'], 'contains': ['864.b1', '864.c1', '864.i1', '864.n1', '864.y1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 526, 1862886], 'label': '3456.oc.432.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935523
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.c1', '144.w1', '216.b1', '216.f1', '216.h1', '216.i1', '216.o1', '216.p1', '216.y1'], 'contains': ['864.b1', '864.e1', '864.m1', '864.q1', '864.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 13412085120], 'label': '3456.oc.432.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935524
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.d1', '144.x1', '216.f1', '216.g1', '216.l1', '216.u1', '216.u2', '216.x1'], 'contains': ['864.b1', '864.f1', '864.n1', '864.r1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693], 'label': '3456.oc.432.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935525
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.e1', '144.y1', '216.c1', '216.g1', '216.i1', '216.j1', '216.q1', '216.r1', '216.y1'], 'contains': ['864.b1', '864.g1', '864.q1', '864.s1', '864.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 13413948379, 1970078819], 'label': '3456.oc.432.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935526
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.bg1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.f1', '144.z1', '216.b1', '216.g1', '216.j1', '216.k1', '216.o1', '216.s1', '216.z1'], 'contains': ['864.b1', '864.t1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 13412085120], 'label': '3456.oc.432.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935527
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.g1', '144.ba1', '216.c1', '216.f1', '216.h1', '216.k1', '216.q1', '216.t1', '216.z1'], 'contains': ['864.b1', '864.u1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 1970078440, 13413948379], 'label': '3456.oc.432.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935528
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.h1', '144.bb1', '216.d1', '216.l1', '216.m1', '216.u1', '216.u2', '216.ba1'], 'contains': ['864.b1', '864.d1', '864.f1', '864.j1', '864.o1', '864.bh1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1134693, 1968627499, 13413948379], 'label': '3456.oc.432.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935529
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.i1', '144.bc1', '216.e1', '216.h1', '216.j1', '216.m1', '216.u2', '216.bb1'], 'contains': ['864.b1', '864.d1', '864.k1', '864.p1', '864.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 1134693, 1968627378], 'label': '3456.oc.432.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935530
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '9.b1'], 'contains': ['36.u1', '36.w1', '36.x1', '36.ba1', '36.bb1', '36.bo1', '36.bq1', '36.bs1', '36.bu1', '36.ch1', '36.ck1', '54.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 13412085385, 526, 2951391], 'label': '3456.oc.18.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935551
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.z1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.cb1', '144.cc1', '216.c1', '216.bg1', '216.bj1', '216.bl1', '216.dh1'], 'contains': ['864.i1', '864.s1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [526, 1968991665, 1134054], 'label': '3456.oc.432.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935531
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.h2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.i2', '144.bc2', '216.e1', '216.i1', '216.k1', '216.m1', '216.u1', '216.bb2'], 'contains': ['864.b1', '864.d1', '864.k2', '864.p2', '864.bl2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627247, 1134693, 13413948127], 'label': '3456.oc.432.h2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.h2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935532
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.j1', '144.bd1', '216.l1', '216.m1', '216.n1', '216.v1', '216.ba1'], 'contains': ['864.b1', '864.c1', '864.j1', '864.w1', '864.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 2588323, 13412085120], 'label': '3456.oc.432.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935533
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.a1', '144.k1', '144.l1', '144.m1', '216.o1', '216.q1', '216.u1', '216.v1', '216.bb1'], 'contains': ['864.a1', '864.b1', '864.k1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588323, 1863007, 13413948127], 'label': '3456.oc.432.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '432.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935534
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '432.j2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.k2', '144.be1', '216.p1', '216.r1', '216.s1', '216.t1', '216.u2', '216.v1', '216.bb2'], 'contains': ['864.b1', '864.k2', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 1863138, 2588323], 'label': '3456.oc.432.j2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.j2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935535
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.n1', '144.bf1', '216.d1', '216.l1', '216.m1', '216.w1', '216.x1'], 'contains': ['864.c1', '864.d1', '864.f1', '864.y1', '864.bc1', '864.bi1', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1967536007, 1862886], 'label': '3456.oc.432.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935536
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.o1', '144.bg1', '216.d1', '216.e1', '216.m1', '216.w1', '216.ba1'], 'contains': ['864.c1', '864.d1', '864.z1', '864.bd1', '864.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1862886, 1969352442, 13414673322], 'label': '3456.oc.432.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935537
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.p1', '144.bh1', '216.d1', '216.l1', '216.bc1'], 'contains': ['864.c1', '864.f1', '864.bb1', '864.be1', '864.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13414673070, 1862886, 1969352190], 'label': '3456.oc.432.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935538
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.q1', '144.r1', '144.s1', '144.bi1', '216.n1', '216.w1', '216.bc1'], 'contains': ['864.c1', '864.bb1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 13414673070, 1862886], 'label': '3456.oc.432.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '432.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 201935539
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.t1', '144.bj1', '216.i1', '216.y1'], 'contains': ['864.d1', '864.e1', '864.g1', '864.bg1', '864.bj1', '864.bq1', '864.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1968627247, 2226652, 13412085120], 'label': '3456.oc.432.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935540
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '432.p1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.bk1', '216.x1', '216.y1', '216.z1', '216.ba1', '216.bb1', '216.bb2'], 'contains': ['864.b1', '864.d1', '864.h1', '864.l1', '864.bk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1134693, 1967535360, 13412085120], 'label': '3456.oc.432.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935541
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '9.b1'], 'contains': ['36.v1', '36.w1', '36.y1', '36.z1', '36.bb1', '36.bp1', '36.br1', '36.bt1', '36.bv1', '36.cj1', '36.cl1', '54.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 2951738, 13412085385, 526], 'label': '3456.oc.18.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935542
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '432.q1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bl1', '216.x1', '216.ba1', '216.bc1'], 'contains': ['864.c1', '864.f1', '864.h1', '864.ba1', '864.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1862886, 1967535360, 13412085120], 'label': '3456.oc.432.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935543
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.r1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1', '144.bm1', '216.y1'], 'contains': ['864.e1', '864.g1', '864.h1', '864.bn1', '864.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2226652, 1967535360, 13412085120], 'label': '3456.oc.432.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.r1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935544
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.s1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.bn1', '144.bp1', '216.d1', '216.n1', '216.bd1', '216.bf1', '216.bh1', '216.cd1', '216.dc1'], 'contains': ['864.i1', '864.j1', '864.y1', '864.z1', '864.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 526, 1862886], 'label': '3456.oc.432.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935545
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.bo1', '144.bq1', '216.e1', '216.v1', '216.be1', '216.bg1', '216.bh1', '216.bi1', '216.cd1'], 'contains': ['864.i1', '864.k1', '864.k2', '864.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [526, 1862886, 13414673191], 'label': '3456.oc.432.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935546
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '432.u1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.br1', '144.bs1', '216.x1', '216.bd1', '216.bi1', '216.bj1', '216.bk1', '216.ce1', '216.dd1'], 'contains': ['864.i1', '864.l1', '864.r1', '864.ba1', '864.bc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [526, 1862886, 1967535360], 'label': '3456.oc.432.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935547
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '432.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.bk1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.bt1', '144.bu1', '216.b1', '216.be1', '216.bj1', '216.bl1', '216.de1'], 'contains': ['864.i1', '864.m1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [265, 1862886, 2226652], 'label': '3456.oc.432.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '432.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935548
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.w1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.bv1', '144.bw1', '216.d1', '216.bh1', '216.ce1', '216.cf1', '216.df1'], 'contains': ['864.i1', '864.o1', '864.bc1', '864.bd1', '864.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 526, 1862886], 'label': '3456.oc.432.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935549
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.x1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.bx1', '144.by1', '216.e1', '216.bf1', '216.bl1', '216.bm1', '216.cf1', '216.dd1'], 'contains': ['864.i1', '864.p1', '864.p2', '864.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1969352563, 526, 1862886], 'label': '3456.oc.432.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935550
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.y1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.bz1', '144.ca1', '216.b1', '216.c1', '216.be1', '216.bg1', '216.bk1', '216.bm1', '216.dg1'], 'contains': ['864.i1', '864.q1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 13413586612, 1862886], 'label': '3456.oc.432.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935552
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '6912.ed', 'aut_weyl_index': 6, 'centralizer': '1152.a1', 'complements': ['864.bn1', '864.bq1', '864.bg1', '864.e1', '864.bj1', '864.g1', '864.h1', '864.bk1', '864.bl2', '864.d1', '864.bm1', '864.bi1', '864.bl1', '864.bh1', '864.bo1', '864.bs1', '864.br1', '864.f1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.e1'], 'contains': ['8.a1', '12.e1', '12.by1', '12.bz1', '12.ca1', '16.f1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [526, 647, 38480884412, 2588323, 13415398178, 1137421, 1862886, 604203618], 'label': '3456.oc.4.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.b1', '2.e1'], 'normal_contains': ['8.a1', '12.e1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '1152.157864'}
-
id: 201935553
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.g1', '9.b1'], 'contains': ['36.a1', '36.x1', '36.z1', '36.bw1', '36.by1', '36.cq1', '36.ct1', '54.c1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39799592190, 13412085385, 1862886, 2951738, 647, 526, 2588323], 'label': '3456.oc.18.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935554
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.ba1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.cd1', '144.cn1', '216.d1', '216.l1', '216.bz1', '216.ca1', '216.cp1', '216.cp2'], 'contains': ['864.j1', '864.n1', '864.o1', '864.bh1', '864.bi1', '864.br1', '864.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13412085767, 1134693, 1968627499], 'label': '3456.oc.432.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935555
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bb1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.co1', '216.ba1', '216.bd1', '216.bz1', '216.cb1', '216.co1', '216.co2'], 'contains': ['864.j1', '864.l1', '864.bh1', '864.bk1', '864.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1134693, 13412085385, 1967535360], 'label': '3456.oc.432.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935556
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.bc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ce1', '144.cs1', '216.i1', '216.p1', '216.be1', '216.bn1', '216.br1', '216.bv1', '216.cg1'], 'contains': ['864.k2', '864.m1', '864.q1', '864.bg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 13413948127], 'label': '3456.oc.432.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935557
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.bd1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cf1', '144.ct1', '216.h1', '216.o1', '216.be1', '216.bo1', '216.bs1', '216.bv1', '216.ch1'], 'contains': ['864.k1', '864.m1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652], 'label': '3456.oc.432.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935558
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.be1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cg1', '144.cu1', '216.e1', '216.u1', '216.bo1', '216.bq1', '216.ca1', '216.co2'], 'contains': ['864.k1', '864.n1', '864.p2', '864.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1968627247, 1134693], 'label': '3456.oc.432.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935559
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.be2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cg2', '144.cu2', '216.e1', '216.u2', '216.bn1', '216.bp1', '216.ca1', '216.co1'], 'contains': ['864.k2', '864.n1', '864.p1', '864.bh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 13413948127, 1968627378], 'label': '3456.oc.432.be2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.be2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935560
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.be3', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cp1', '216.m1', '216.bf1', '216.ca1', '216.co1', '216.cp1'], 'contains': ['864.j1', '864.p1', '864.bh1', '864.bl2', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1134693, 13412085385, 1968627378], 'label': '3456.oc.432.be3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.be3', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935561
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.be4', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cp2', '216.m1', '216.bf1', '216.ca1', '216.co2', '216.cp2'], 'contains': ['864.j1', '864.p2', '864.bh1', '864.bl1', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627247, 1134693, 13412085385], 'label': '3456.oc.432.be4', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.be4', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.be4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935562
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bf1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cq1', '216.l1', '216.bd1', '216.cc1', '216.cp1', '216.cp2'], 'contains': ['864.j1', '864.r1', '864.bi1', '864.bm1', '864.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 1134693, 13412085385], 'label': '3456.oc.432.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bf1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935563
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.bg1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ci1', '144.cv1', '216.i1', '216.r1', '216.bg1', '216.bp1', '216.br1', '216.bw1', '216.ci1'], 'contains': ['864.k2', '864.q1', '864.s1', '864.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 1970078819, 13413219692], 'label': '3456.oc.432.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935564
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.h1', '6.i1', '6.j1', '9.b1'], 'contains': ['36.a1', '36.y1', '36.ba1', '36.bx1', '36.bz1', '36.cs1', '36.cw1', '54.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085385, 39799592190, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.18.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935565
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.bh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ch1', '144.cx1', '216.j1', '216.o1', '216.be1', '216.bq1', '216.bt1', '216.bw1', '216.cj1'], 'contains': ['864.k1', '864.q1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738], 'label': '3456.oc.432.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bh1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935566
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.bi1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cj1', '144.cw1', '216.h1', '216.q1', '216.bg1', '216.bq1', '216.bt1', '216.bv1', '216.ck1'], 'contains': ['864.k1', '864.q1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 1970078440, 13414673322], 'label': '3456.oc.432.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bi1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935567
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.bj1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ck1', '144.cy1', '216.j1', '216.q1', '216.bg1', '216.bo1', '216.bs1', '216.bw1', '216.cl1'], 'contains': ['864.k1', '864.s1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 1970078819, 13414673322], 'label': '3456.oc.432.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bj1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935568
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.bk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.bg1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cl1', '144.cz1', '216.k1', '216.s1', '216.be1', '216.bp1', '216.bu1', '216.bw1', '216.cg1'], 'contains': ['864.k2', '864.t1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 13413948127], 'label': '3456.oc.432.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bk1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935569
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.bl1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.cm1', '144.da1', '216.k1', '216.t1', '216.bg1', '216.bn1', '216.bu1', '216.bv1', '216.ci1'], 'contains': ['864.k2', '864.u1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1863259, 1970078440, 13413219692], 'label': '3456.oc.432.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bl1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935627
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.dg1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.go1', '216.ba1', '216.bd1', '216.bi1', '216.cb1', '216.dl1'], 'contains': ['864.z1', '864.ba1', '864.bk1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1862886, 13414673322, 1967535360], 'label': '3456.oc.432.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935570
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bm1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.cr1', '144.db1', '216.m1', '216.u1', '216.bh1', '216.ca1', '216.cb1', '216.cc1', '216.cp1'], 'contains': ['864.j1', '864.k1', '864.o1', '864.bh1', '864.bi1', '864.bl2', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1134693, 13412085385, 1968627499], 'label': '3456.oc.432.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935571
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bm2', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.cr2', '144.db2', '216.m1', '216.u2', '216.bh1', '216.ca1', '216.cb1', '216.cc1', '216.cp2'], 'contains': ['864.j1', '864.k2', '864.o1', '864.bh1', '864.bi1', '864.bl1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1134693, 1968627499, 13413948127], 'label': '3456.oc.432.bm2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.bm2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bm2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935572
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.bn1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dc1', '216.bb1', '216.bi1', '216.bs1', '216.bt1', '216.cb1', '216.co2'], 'contains': ['864.k1', '864.l1', '864.bk1', '864.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13413948258, 1134693, 1967535360], 'label': '3456.oc.432.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935573
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.bn2', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dc2', '216.bb2', '216.bi1', '216.br1', '216.bu1', '216.cb1', '216.co1'], 'contains': ['864.k2', '864.l1', '864.bk1', '864.bl2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1134693, 13413948127, 1967535360], 'label': '3456.oc.432.bn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bn2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bn2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935574
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bo1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.dd1', '144.dd2', '216.u1', '216.u2', '216.bi1', '216.bv1', '216.bw1', '216.cc1'], 'contains': ['864.k1', '864.k2', '864.r1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1134693, 13413948127], 'label': '3456.oc.432.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bo1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935575
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.l1', '9.b1'], 'contains': ['36.c1', '36.e1', '36.f1', '36.g1', '36.i1', '36.j1', '36.r1', '36.t1', '36.u1', '36.v1', '36.x1', '36.y1', '36.bc1', '36.be1', '36.bf1', '36.bg1', '36.bh1', '36.bi1', '36.bk1', '36.bl1', '36.bm1', '36.cb1', '36.cd1', '54.e1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 13413948127, 2951391], 'label': '3456.oc.18.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935576
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.bp1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.de1', '144.df1', '216.y1', '216.bj1', '216.br1', '216.bs1', '216.bx1', '216.cq1', '216.cr1'], 'contains': ['864.l1', '864.m1', '864.s1', '864.bn1', '864.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2226652, 1967535360], 'label': '3456.oc.432.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bp1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935577
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.bq1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dg1', '216.x1', '216.bx1', '216.by1', '216.bz1', '216.co1', '216.co2'], 'contains': ['864.l1', '864.n1', '864.bo1', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085767, 1134693, 1967535360], 'label': '3456.oc.432.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bq1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935578
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.br1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dh1', '216.y1', '216.bk1', '216.br1', '216.bt1', '216.by1', '216.cs1', '216.ct1'], 'contains': ['864.l1', '864.q1', '864.bp1', '864.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 13414311772, 1967535360], 'label': '3456.oc.432.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935579
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.bs1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.di1', '144.dk1', '216.z1', '216.bj1', '216.bt1', '216.bu1', '216.by1', '216.cq1', '216.cu1'], 'contains': ['864.l1', '864.t1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2951738, 1967535360], 'label': '3456.oc.432.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935580
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bt1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dj1', '216.z1', '216.bk1', '216.bs1', '216.bu1', '216.bx1', '216.cs1', '216.cv1'], 'contains': ['864.l1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13415036858, 1134693, 1967535360], 'label': '3456.oc.432.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bt1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935581
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.bu1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.dl1', '144.dm1', '216.b1', '216.f1', '216.bn1', '216.bo1', '216.bx1', '216.cg1', '216.ch1'], 'contains': ['864.m1', '864.n1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652], 'label': '3456.oc.432.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935582
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bv1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dn1', '144.do1', '216.i1', '216.bl1', '216.bo1', '216.cr1', '216.cw1'], 'contains': ['864.m1', '864.p2', '864.s1', '864.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627247, 1134693, 2226652], 'label': '3456.oc.432.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bv1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935583
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bw1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dp1', '144.dq1', '216.h1', '216.bl1', '216.bn1', '216.cq1', '216.cx1'], 'contains': ['864.m1', '864.p1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2226652, 1968627378], 'label': '3456.oc.432.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935584
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.bx1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.dr1', '144.ds1', '216.f1', '216.bj1', '216.bv1', '216.cw1', '216.cx1'], 'contains': ['864.m1', '864.r1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1134693, 2226652], 'label': '3456.oc.432.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935585
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.by1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.dt1', '144.dx1', '216.b1', '216.g1', '216.bp1', '216.bq1', '216.by1', '216.cg1', '216.cj1'], 'contains': ['864.n1', '864.q1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738], 'label': '3456.oc.432.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.by1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935586
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.m1', '9.b1'], 'contains': ['36.h1', '36.k1', '36.l1', '36.w1', '36.z1', '36.ba1', '36.bg1', '36.bh1', '36.bn1', '36.ce1', '36.cf1', '54.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 1968627499, 526, 13413948127], 'label': '3456.oc.18.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935587
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.bz1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.du1', '144.dw1', '216.c1', '216.f1', '216.bn1', '216.bq1', '216.by1', '216.ci1', '216.ck1'], 'contains': ['864.n1', '864.q1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078440], 'label': '3456.oc.432.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.bz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935588
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.ca1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.dv1', '144.dy1', '216.c1', '216.g1', '216.bo1', '216.bp1', '216.bx1', '216.ci1', '216.cl1'], 'contains': ['864.n1', '864.s1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078819], 'label': '3456.oc.432.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ca1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935589
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.cb1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.dz1', '144.ea1', '216.h1', '216.j1', '216.bm1', '216.bn1', '216.bp1', '216.cs1', '216.cy1'], 'contains': ['864.p1', '864.q1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1134693, 13414311772, 1968627378], 'label': '3456.oc.432.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935590
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.cc1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.eb1', '216.i1', '216.bm1', '216.bq1', '216.ct1', '216.cy2'], 'contains': ['864.p2', '864.q1', '864.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627247, 1134693, 13414311772], 'label': '3456.oc.432.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935591
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.cd1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ec1', '144.ed1', '216.j1', '216.bl1', '216.bp1', '216.cq1', '216.cz1'], 'contains': ['864.p1', '864.s1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2951738, 1968627378], 'label': '3456.oc.432.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935592
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.ce1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ee1', '144.eg1', '216.k1', '216.bl1', '216.bq1', '216.cu1', '216.cw1'], 'contains': ['864.p2', '864.t1', '864.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738], 'label': '3456.oc.432.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ce1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935593
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.cf1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ef1', '216.k1', '216.bm1', '216.bo1', '216.cv1', '216.cy2'], 'contains': ['864.p2', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627247, 13415036858, 1134693], 'label': '3456.oc.432.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935594
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.cg1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.eh1', '144.ei1', '216.f1', '216.g1', '216.bk1', '216.bv1', '216.bw1', '216.cy1', '216.cy2'], 'contains': ['864.q1', '864.r1', '864.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 1134693, 13414311772], 'label': '3456.oc.432.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cg1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935595
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.ch1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ej1', '144.ek1', '216.g1', '216.bj1', '216.bw1', '216.cw1', '216.cz1'], 'contains': ['864.r1', '864.s1', '864.t1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738], 'label': '3456.oc.432.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ch1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935596
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.ci1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.el1', '144.en1', '216.l1', '216.n1', '216.bz1', '216.ca1', '216.dc1'], 'contains': ['864.j1', '864.n1', '864.w1', '864.y1', '864.bb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323], 'label': '3456.oc.432.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ci1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935597
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.k1', '9.b1'], 'contains': ['36.a1', '36.d1', '36.m1', '36.n1', '36.s1', '36.bb1', '36.bd1', '36.bh1', '36.bj1', '36.ca1', '36.co1', '54.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967536007, 13412085385, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935598
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.cj1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.em1', '144.eo1', '216.m1', '216.v1', '216.ca1', '216.cb1', '216.cc1', '216.cd1', '216.dc1'], 'contains': ['864.j1', '864.k1', '864.k2', '864.w1', '864.y1', '864.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085385, 1862886, 2588323], 'label': '3456.oc.432.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935599
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.ck1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ep1', '144.eq1', '216.ba1', '216.bz1', '216.cb1', '216.ce1', '216.dd1'], 'contains': ['864.l1', '864.o1', '864.w1', '864.ba1', '864.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1862886, 2588323, 1967535360], 'label': '3456.oc.432.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ck1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935600
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.cl1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.er1', '144.es1', '216.l1', '216.cc1', '216.ce1', '216.df1'], 'contains': ['864.o1', '864.r1', '864.w1', '864.bc1', '864.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1862886, 2588323], 'label': '3456.oc.432.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935601
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.cm1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.et1', '144.eu1', '216.m1', '216.ca1', '216.cf1', '216.dd1', '216.df1'], 'contains': ['864.o1', '864.p1', '864.p2', '864.w1', '864.bc1', '864.bd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967535625, 1862886, 2588323], 'label': '3456.oc.432.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935602
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '432.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ev1', '144.ew1', '216.a1', '216.n1', '216.cd1', '216.ce1', '216.cf1'], 'contains': ['864.i1', '864.w1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 526, 1862886], 'label': '3456.oc.432.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '432.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935603
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.co1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ex1', '144.ey1', '216.u1', '216.v1', '216.cg1', '216.ci1', '216.co1', '216.cp2', '216.dc1'], 'contains': ['864.a1', '864.j1', '864.k2', '864.n1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 2588323, 1863007], 'label': '3456.oc.432.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.co1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935604
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.co2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ex2', '144.ey2', '216.u2', '216.v1', '216.ch1', '216.cj1', '216.ck1', '216.cl1', '216.cm1', '216.cn1', '216.co2', '216.cp1', '216.dc1'], 'contains': ['864.j1', '864.k1', '864.n1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 1863138, 2588323], 'label': '3456.oc.432.co2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.co2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.co2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935605
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '432.cp1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.ez1', '144.fa1', '144.fb1', '216.bb1', '216.co1', '216.cq1', '216.cs1', '216.dd1'], 'contains': ['864.a1', '864.l1', '864.p1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2588323, 1863007, 1967535360], 'label': '3456.oc.432.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '432.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935606
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '432.cp2', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fa2', '144.fb2', '216.bb2', '216.co2', '216.cr1', '216.ct1', '216.cu1', '216.cv1', '216.dd1'], 'contains': ['864.l1', '864.p2', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1863138, 2588323, 1967535360], 'label': '3456.oc.432.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cp2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cp2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935607
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '432.cq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '24.bk1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fc1', '144.fd1', '144.fg1', '216.o1', '216.cg1', '216.cq1', '216.cw1', '216.de1'], 'contains': ['864.a1', '864.m1', '864.t1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2226652, 2588323, 1863007], 'label': '3456.oc.432.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '432.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cq1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935628
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.dh1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.gp1', '216.m1', '216.bh1', '216.bi1', '216.cc1', '216.dm1'], 'contains': ['864.z1', '864.bc1', '864.bl1', '864.bl2', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 1862886, 13414673322], 'label': '3456.oc.432.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935608
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.n1', '9.b1'], 'contains': ['36.bl1', '36.bn1', '36.bo1', '36.br1', '36.bs1', '36.bv1', '36.bw1', '36.bz1', '36.ca1', '36.cb1', '36.cf1', '54.h1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 13412085385, 1968627499, 526, 2951391], 'label': '3456.oc.18.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935609
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '432.cr1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '12.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fe1', '144.ff1', '216.p1', '216.ch1', '216.cr1', '216.cx1', '216.de1'], 'contains': ['864.m1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2588202, 2226652, 1863007], 'label': '3456.oc.432.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cr1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201935610
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.cs1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fh1', '144.fi1', '216.u1', '216.cp2', '216.cw1', '216.cy2', '216.dd1', '216.df1'], 'contains': ['864.a1', '864.o1', '864.p2', '864.r1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1967536007, 2588323, 1863007], 'label': '3456.oc.432.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935611
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.cs2', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fh2', '144.fi2', '216.u2', '216.cp1', '216.cx1', '216.cy1', '216.cz1', '216.da1', '216.db1', '216.dd1', '216.df1'], 'contains': ['864.o1', '864.p1', '864.r1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1967536007, 1863138, 2588323], 'label': '3456.oc.432.cs2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cs2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cs2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935612
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.ct1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.fj1', '144.fl1', '144.fm1', '144.fn1', '216.o1', '216.q1', '216.cg1', '216.ci1', '216.cs1', '216.cy2', '216.dg1'], 'contains': ['864.a1', '864.q1', '864.u1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413586612, 2588323, 1863007], 'label': '3456.oc.432.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '432.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.ct1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935613
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.cu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fk1', '144.fo1', '216.p1', '216.r1', '216.cj1', '216.ck1', '216.ct1', '216.cy1', '216.dg1'], 'contains': ['864.q1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413586379, 2588202, 1863007], 'label': '3456.oc.432.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cu1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935614
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.cv1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fp1', '144.fq1', '144.fr1', '144.fs1', '144.ft1', '216.q1', '216.ci1', '216.cq1', '216.cw1', '216.dh1'], 'contains': ['864.a1', '864.s1', '864.v1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968991665, 2588323, 1863007], 'label': '3456.oc.432.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '432.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cv1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935615
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.cw1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fu1', '144.fv1', '216.r1', '216.cl1', '216.cr1', '216.cz1', '216.dh1'], 'contains': ['864.s1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1863259, 2588071, 1969714258], 'label': '3456.oc.432.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935616
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '432.cx1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '12.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fw1', '144.ga1', '216.s1', '216.cj1', '216.cm1', '216.cu1', '216.cz1', '216.da1', '216.de1', '216.di1'], 'contains': ['864.t1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [2588202, 2951738, 1863007], 'label': '3456.oc.432.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cx1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935617
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '432.cy1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '36.bg1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.fx1', '144.fy1', '216.s1', '216.t1', '216.ch1', '216.cl1', '216.cm1', '216.cn1', '216.cv1', '216.cy1', '216.db1', '216.dg1', '216.dj1'], 'contains': ['864.u1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 1863007, 13415398178], 'label': '3456.oc.432.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '432.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cy1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935618
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.cz1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.fz1', '144.gb1', '216.t1', '216.ck1', '216.cn1', '216.cu1', '216.cx1', '216.da1', '216.dh1', '216.dk1'], 'contains': ['864.v1', '864.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2588071, 1968991665], 'label': '3456.oc.432.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '432.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.cz1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201935619
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.o1', '9.b1'], 'contains': ['36.bm1', '36.bn1', '36.bp1', '36.bq1', '36.bt1', '36.bu1', '36.bx1', '36.by1', '36.ca1', '36.cd1', '36.ce1', '54.i1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 13412085385, 1968627499, 526], 'label': '3456.oc.18.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935620
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '432.da1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.gc1', '144.gd1', '216.a1', '216.v1', '216.dc1', '216.dd1', '216.de1', '216.df1', '216.dg1', '216.dh1', '216.di1', '216.dj1', '216.dk1'], 'contains': ['864.a1', '864.i1', '864.w1', '864.x1'], 'core': '864.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [526, 1862886, 2588323], 'label': '3456.oc.432.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '432.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.da1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935621
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.db1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.ge1', '144.gg1', '216.d1', '216.w1', '216.bf1', '216.bz1', '216.ca1'], 'contains': ['864.y1', '864.bb1', '864.bd1', '864.bh1', '864.br1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13414673070, 1862886, 1969352442], 'label': '3456.oc.432.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.db1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935622
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.dc1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.gh1', '216.x1', '216.bd1', '216.bz1', '216.cb1', '216.dl1'], 'contains': ['864.y1', '864.ba1', '864.bi1', '864.bk1', '864.bo1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085385, 1862886, 1967535360], 'label': '3456.oc.432.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935623
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.dd1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.gf1', '144.gl1', '216.l1', '216.w1', '216.bd1', '216.bh1', '216.ca1'], 'contains': ['864.z1', '864.bb1', '864.bc1', '864.bh1', '864.bi1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13414673070, 1862886], 'label': '3456.oc.432.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935624
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.dd2', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.gi1', '216.d1', '216.bd1', '216.ca1', '216.cc1', '216.dm1'], 'contains': ['864.y1', '864.bc1', '864.bh1', '864.bm1', '864.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13412085385, 1862886], 'label': '3456.oc.432.dd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dd2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dd2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935625
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.de1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['144.gj1', '144.gm1', '216.e1', '216.m1', '216.bf1', '216.bh1', '216.ca1', '216.cb1', '216.dm1'], 'contains': ['864.y1', '864.z1', '864.bd1', '864.bh1', '864.bl1', '864.bl2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13412085385, 1862886, 1969352442], 'label': '3456.oc.432.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.de1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935626
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.df1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.gk1', '144.gn1', '216.d1', '216.l1', '216.bh1', '216.cc1', '216.dl1'], 'contains': ['864.y1', '864.z1', '864.be1', '864.bi1', '864.bm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085385, 1862886, 1969352190], 'label': '3456.oc.432.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.df1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935629
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.di1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gq1', '216.bc1', '216.bd1', '216.bz1'], 'contains': ['864.ba1', '864.bb1', '864.bo1', '864.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13414673070, 1862886, 1967535360], 'label': '3456.oc.432.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.di1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935630
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1', '6.q1', '9.a1'], 'contains': ['36.b1', '36.cn1', '36.cy1', '54.j1', '72.ep1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1137421, 2951738, 1967901282, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935631
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '432.dj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.gr1', '144.gs1', '216.n1', '216.w1', '216.cd1', '216.dl1', '216.dm1'], 'contains': ['864.y1', '864.z1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 13412085385, 1862886], 'label': '3456.oc.432.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '432.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935632
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '432.dk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gt1', '144.gu1', '144.gv1', '216.bc1', '216.ce1', '216.dl1'], 'contains': ['864.ba1', '864.be1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2587950, 1862886, 1969352190], 'label': '3456.oc.432.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1', 'old_label': '432.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dk1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 201935633
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '432.dl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.gw1', '144.gx1', '216.w1', '216.ce1', '216.cf1', '216.dm1'], 'contains': ['864.bc1', '864.bd1', '864.bf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2587950, 1967536007, 1862886], 'label': '3456.oc.432.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '432.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935634
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '432.dm1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['144.gy1', '216.y1', '216.br1'], 'contains': ['864.bg1', '864.bj1', '864.bk1', '864.bn1', '864.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2226652, 13413948127, 1967535360], 'label': '3456.oc.432.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935635
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '432.dn1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['144.gz1', '216.i1', '216.br1'], 'contains': ['864.bg1', '864.bj1', '864.bl2', '864.bq1', '864.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [1968627247, 2226652, 13413219813], 'label': '3456.oc.432.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '432.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.dn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935636
{'ambient': '3456.oc', 'aut_centralizer_order': 3456, 'aut_label': '576.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '6.a1', 'complements': ['6.p1', '6.q1', '6.a1', '6.h1', '6.i1', '6.r1'], 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '192.d1', '192.e1', '288.l1', '288.m1', '288.n1', '288.o1', '288.p1', '288.q1', '288.r1'], 'contains': ['1152.a1', '1728.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [39797775360, 13412085120], 'label': '3456.oc.576.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': ['144.a1', '192.a1'], 'normal_contains': ['1152.a1'], 'normalizer': '1.a1', 'old_label': '576.a1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '288.1035', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '576.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935637
{'ambient': '3456.oc', 'aut_centralizer_order': 3456, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.a1', '192.c1', '288.b1', '288.c1', '288.d1', '288.e1', '288.g1', '288.h1', '288.r1'], 'contains': ['1152.a1', '1728.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480520960, 13412085120], 'label': '3456.oc.576.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '576.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935638
{'ambient': '3456.oc', 'aut_centralizer_order': 216, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '96.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.l1', '144.r1', '192.c1', '192.d1', '288.f1', '288.i1', '288.k1'], 'contains': ['1152.c1', '1728.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137421, 13412085120], 'label': '3456.oc.576.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '576.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935639
{'ambient': '3456.oc', 'aut_centralizer_order': 108, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.m1', '144.s1', '192.c1', '192.e1', '288.j1'], 'contains': ['1152.d1', '1728.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [38482336681, 13412085120], 'label': '3456.oc.576.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.d1', 'old_label': '576.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935640
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '6.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.f1', '288.a1', '288.b1', '288.l1', '288.s1', '288.u1', '288.v1', '288.v2', '288.w1', '288.x1', '288.x2', '288.y1', '288.ba1', '288.bc1', '288.bd1', '288.be1', '288.bg1', '288.bg2', '288.bi1', '288.bj1', '288.bk1', '288.bm1', '288.bo1', '288.bp1', '288.bq1', '288.br1', '288.bu1', '288.bw1'], 'contains': ['1152.a1', '1728.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 38480884533], 'label': '3456.oc.576.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935641
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.r1', '9.a1'], 'contains': ['36.cn1', '36.cu1', '54.k1', '72.eq1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967901282, 1862886, 647, 13415398178, 526, 2588323, 1137421], 'label': '3456.oc.18.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935642
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '576.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '12.bw1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['192.f1', '288.t1', '288.z1', '288.bb1', '288.bf1', '288.bh1', '288.bh2', '288.bl1', '288.bn1', '288.bs1', '288.bt1', '288.bv1', '288.bx1', '288.bx2'], 'contains': ['1152.b1', '1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 37882213173], 'label': '3456.oc.576.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '576.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935643
{'ambient': '3456.oc', 'aut_centralizer_order': 1728, 'aut_label': '576.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.g1', '288.c1', '288.m1', '288.s1', '288.bu1', '288.cb1', '288.cc1', '288.cd1', '288.ce1', '288.cf1', '288.ch1', '288.ci1', '288.cj1', '288.cl1', '288.cn1', '288.cp1'], 'contains': ['1152.a1', '1728.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [38481612726, 1862886], 'label': '3456.oc.576.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '576.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935644
{'ambient': '3456.oc', 'aut_centralizer_order': 1728, 'aut_label': '576.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.g1', '288.t1', '288.bv1', '288.cg1', '288.ck1', '288.cm1', '288.co1', '288.cq1'], 'contains': ['1152.b1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37882941366, 1862886], 'label': '3456.oc.576.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '576.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935645
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '576.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.h1', '288.b1', '288.n1', '288.u1', '288.v1', '288.v2', '288.cb1', '288.cc1', '288.cu1', '288.cv1', '288.cw1', '288.cx1', '288.dc1', '288.dd1', '288.dd2', '288.de1'], 'contains': ['1152.a1', '1728.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480520960, 13413948127], 'label': '3456.oc.576.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '576.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935646
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '576.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.h1', '288.d1', '288.l1', '288.w1', '288.x1', '288.x2', '288.cd1', '288.ce1', '288.cy1', '288.cz1', '288.da1', '288.db1', '288.dc1', '288.dd1', '288.dd2', '288.de1'], 'contains': ['1152.a1', '1728.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39797775360, 13413948127], 'label': '3456.oc.576.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '576.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935647
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '576.k1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '288.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ez1', '144.gt1', '192.i1', '192.j1', '288.k1', '288.df1', '288.dg1'], 'contains': ['1152.c1', '1728.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1967901282, 1137042], 'label': '3456.oc.576.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '576.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935648
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '576.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.b1', '192.i1', '288.r1', '288.y1', '288.cf1', '288.dc1', '288.dh1', '288.dj1', '288.dk1'], 'contains': ['1152.a1', '1728.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480520960, 1967535360], 'label': '3456.oc.576.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '576.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935649
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '576.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1', '192.j1', '288.z1', '288.cg1', '288.di1'], 'contains': ['1152.b1', '1728.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37881446400, 1967535360], 'label': '3456.oc.576.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '576.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935650
{'ambient': '3456.oc', 'aut_centralizer_order': 864, 'aut_label': '576.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '24.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.k1', '192.l1', '288.e1', '288.o1', '288.ba1', '288.cu1', '288.cy1', '288.dh1', '288.dl1'], 'contains': ['1152.a1', '1728.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [38480520960, 2226652], 'label': '3456.oc.576.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '576.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935651
{'ambient': '3456.oc', 'aut_centralizer_order': 864, 'aut_label': '576.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.k1', '192.m1', '288.bb1', '288.di1', '288.dm1'], 'contains': ['1152.b1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [37881446400, 2226652], 'label': '3456.oc.576.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.dd1', 'old_label': '576.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935652
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.p1', '6.s1', '9.b1'], 'contains': ['36.cb1', '36.ce1', '36.ch1', '36.cl1', '36.co1', '36.cq1', '36.cw1', '54.j1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1967536007, 2951738, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935653
{'ambient': '3456.oc', 'aut_centralizer_order': 432, 'aut_label': '576.p1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fg1', '192.l1', '192.m1', '288.f1', '288.df1'], 'contains': ['1152.c1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1137042, 2226652], 'label': '3456.oc.576.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '576.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935654
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '576.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.n1', '288.c1', '288.p1', '288.u1', '288.bc1', '288.cb1', '288.ch1', '288.cz1', '288.da1', '288.dj1', '288.dn1', '288.do1'], 'contains': ['1152.a1', '1728.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085385, 38480520960], 'label': '3456.oc.576.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '576.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935655
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '576.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.n1', '288.g1', '288.m1', '288.w1', '288.bd1', '288.cd1', '288.ci1', '288.cv1', '288.cw1', '288.dj1', '288.dn1', '288.do1'], 'contains': ['1152.a1', '1728.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13412085385, 39797775360], 'label': '3456.oc.576.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '576.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935656
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '576.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['192.o1', '288.d1', '288.n1', '288.y1', '288.be1', '288.bg1', '288.bg2', '288.cj1', '288.cl1', '288.cv1', '288.cz1', '288.dd1', '288.dd2', '288.dl1', '288.dn1', '288.dp1'], 'contains': ['1152.a1', '1728.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627499, 38480520960], 'label': '3456.oc.576.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '576.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935657
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '576.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['192.o1', '288.z1', '288.bf1', '288.bh1', '288.bh2', '288.ck1', '288.cm1', '288.dm1'], 'contains': ['1152.b1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [37881446400, 1968627499], 'label': '3456.oc.576.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '576.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935658
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '576.u1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.p1', '192.q1', '192.r1', '288.e1', '288.q1', '288.bi1', '288.cu1', '288.db1', '288.dk1', '288.dp1'], 'contains': ['1152.a1', '1728.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13414311772, 38480520960], 'label': '3456.oc.576.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '576.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935659
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '576.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.r1', '192.s1', '288.h1', '288.o1', '288.bj1', '288.cx1', '288.cy1', '288.dk1', '288.dp1'], 'contains': ['1152.a1', '1728.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39797775360, 13414311772], 'label': '3456.oc.576.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '576.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935660
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '576.w1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fm1', '192.p1', '192.s1', '288.f1', '288.i1', '288.dg1'], 'contains': ['1152.c1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [13414311772, 1137042], 'label': '3456.oc.576.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '576.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.w1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935661
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '576.x1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fn1', '192.q1', '192.s1', '288.j1'], 'contains': ['1152.d1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [39798141282, 13414311772], 'label': '3456.oc.576.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.l1', 'old_label': '576.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935662
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '576.y1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.t1', '288.g1', '288.p1', '288.be1', '288.bk1', '288.cf1', '288.cj1', '288.cn1', '288.cw1', '288.da1', '288.de1', '288.do1'], 'contains': ['1152.a1', '1728.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 38480520960], 'label': '3456.oc.576.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '576.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935663
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '41472.kr', 'aut_weyl_index': 1, 'centralizer': '3456.a1', 'complements': ['864.e1', '864.bg1', '864.h1', '864.d1', '864.bk1', '864.bl2', '864.bo1', '864.f1', '864.bs1', '864.bh1', '864.br1', '864.bi1', '864.bm1', '864.bl1', '864.bp1', '864.bt1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.a1', '12.cb1', '12.cc1', '12.cd1', '12.ce1', '12.cf1', '16.g1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1137421, 38480884412, 526, 647, 1862886, 1968991665, 2588323, 604203618], 'label': '3456.oc.4.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
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id: 201935664
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1', '6.s1'], 'contains': ['36.cc1', '36.cg1', '36.ci1', '36.cm1', '36.cp1', '36.cr1', '36.cx1', '54.j1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37882213052, 1967536007, 2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.18.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '18.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935665
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '576.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.t1', '288.bf1', '288.bl1', '288.cg1', '288.ck1', '288.co1'], 'contains': ['1152.b1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 37881446400], 'label': '3456.oc.576.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '576.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935666
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '576.ba1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['192.u1', '192.v1', '192.w1', '288.h1', '288.q1', '288.bm1', '288.cx1', '288.db1', '288.dh1', '288.dl1'], 'contains': ['1152.a1', '1728.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38480520960, 1970078819], 'label': '3456.oc.576.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '576.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935667
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '576.bb1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.w1', '192.x1', '192.y1', '288.bn1', '288.di1', '288.dm1'], 'contains': ['1152.b1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [37881446400, 1970078819], 'label': '3456.oc.576.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.eu1', 'old_label': '576.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935668
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '576.bc1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.fr1', '192.u1', '192.x1', '288.i1', '288.df1'], 'contains': ['1152.c1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1137042, 1970078819], 'label': '3456.oc.576.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '576.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935669
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '576.bd1', 'aut_quo_index': None, 'aut_stab_index': 576, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['144.fs1', '192.u1', '192.v1', '192.y1', '288.j1'], 'contains': ['1152.d1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [38482336575, 1970078819], 'label': '3456.oc.576.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '288.j1', 'old_label': '576.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935670
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '576.be1', 'aut_quo_index': None, 'aut_stab_index': 576, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.ft1', '192.v1', '192.x1', '192.y1'], 'contains': ['1152.e1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 576, 'diagramx': None, 'generators': [37883665215, 1970078819], 'label': '3456.oc.576.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '576.be1', 'old_label': '576.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201935671
{'ambient': '3456.oc', 'aut_centralizer_order': 2304, 'aut_label': '864.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '6.b1', 'complements': ['4.f1'], 'conjugacy_class_count': 3, 'contained_in': ['288.a1', '288.bx1', '288.by1', '288.bz1', '288.ca1', '432.j1', '432.co1', '432.cp1', '432.cq1', '432.cs1', '432.ct1', '432.cv1', '432.da1'], 'contains': ['1728.b1'], 'core': '864.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2588323, 1863007], 'label': '3456.oc.864.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': ['216.a1', '288.a1'], 'normal_contains': ['3456.a1'], 'normalizer': '1.a1', 'old_label': '864.a1', 'projective_image': '3456.oc', 'quotient_action_image': '6.1', 'quotient_action_kernel': '144.192', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '864.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935672
{'ambient': '3456.oc', 'aut_centralizer_order': 768, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.b1', '288.l1', '432.a1', '432.b1', '432.c1', '432.d1', '432.e1', '432.f1', '432.g1', '432.h1', '432.h2', '432.i1', '432.j1', '432.j2', '432.p1'], 'contains': ['1728.a1', '1728.b1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 13412085120], 'label': '3456.oc.864.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935673
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.c1', '288.m1', '432.a1', '432.i1', '432.k1', '432.l1', '432.m1', '432.n1', '432.q1'], 'contains': ['1728.a1', '1728.c1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1862886, 13412085120], 'label': '3456.oc.864.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935674
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.d1', '288.n1', '432.g1', '432.h1', '432.h2', '432.k1', '432.l1', '432.o1', '432.p1'], 'contains': ['1728.a1', '1728.d1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627499, 13413948379], 'label': '3456.oc.864.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935675
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.r1', '6.t1', '9.b1'], 'contains': ['36.cd1', '36.cf1', '36.cj1', '36.ck1', '36.co1', '36.cs1', '36.ct1', '54.k1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 647, 13415398178, 1967536007, 2588323, 526, 38480884412], 'label': '3456.oc.18.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935676
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.e1', '288.f1', '288.o1', '432.b1', '432.o1', '432.r1'], 'contains': ['1728.a1', '1728.f1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2226652, 13412085120], 'label': '3456.oc.864.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '864.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935677
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.g1', '288.p1', '432.c1', '432.g1', '432.k1', '432.m1', '432.q1'], 'contains': ['1728.a1', '1728.g1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1967536007], 'label': '3456.oc.864.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935678
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.g1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.h1', '288.i1', '288.j1', '288.q1', '432.d1', '432.o1', '432.r1'], 'contains': ['1728.a1', '1728.i1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1970078819, 13412085120], 'label': '3456.oc.864.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935679
{'ambient': '3456.oc', 'aut_centralizer_order': 2304, 'aut_label': '864.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.k1', '288.r1', '432.p1', '432.q1', '432.r1'], 'contains': ['1728.a1', '1728.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967535360, 13412085120], 'label': '3456.oc.864.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '864.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935680
{'ambient': '3456.oc', 'aut_centralizer_order': 2304, 'aut_label': '864.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.s1', '288.t1', '432.a1', '432.s1', '432.t1', '432.u1', '432.v1', '432.w1', '432.x1', '432.y1', '432.z1', '432.cn1', '432.da1'], 'contains': ['1728.b1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [526, 1862886], 'label': '3456.oc.864.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935681
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.j1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['288.u1', '288.w1', '432.g1', '432.i1', '432.s1', '432.ba1', '432.bb1', '432.be3', '432.be4', '432.bf1', '432.bm1', '432.bm2', '432.ci1', '432.cj1', '432.co1', '432.co2'], 'contains': ['1728.b1', '1728.d1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 13412085385], 'label': '3456.oc.864.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935682
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.v1', '288.x1', '432.h1', '432.j1', '432.t1', '432.bd1', '432.be1', '432.bh1', '432.bi1', '432.bj1', '432.bm1', '432.bn1', '432.bo1', '432.cj1', '432.co2'], 'contains': ['1728.b1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1134693], 'label': '3456.oc.864.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935683
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.k2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.v2', '288.x2', '432.h2', '432.j2', '432.t1', '432.bc1', '432.be2', '432.bg1', '432.bk1', '432.bl1', '432.bm2', '432.bn2', '432.bo1', '432.cj1', '432.co1'], 'contains': ['1728.b1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 13413948127], 'label': '3456.oc.864.k2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.k2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.k2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935684
{'ambient': '3456.oc', 'aut_centralizer_order': 512, 'aut_label': '864.l1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.y1', '288.z1', '432.p1', '432.u1', '432.bb1', '432.bn1', '432.bn2', '432.bp1', '432.bq1', '432.br1', '432.bs1', '432.bt1', '432.ck1', '432.cp1', '432.cp2'], 'contains': ['1728.b1', '1728.e1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1134693, 1967535360], 'label': '3456.oc.864.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935685
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '864.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '12.w1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.ba1', '288.bb1', '432.b1', '432.v1', '432.bc1', '432.bd1', '432.bp1', '432.bu1', '432.bv1', '432.bw1', '432.bx1', '432.cq1', '432.cr1'], 'contains': ['1728.b1', '1728.f1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 2226652], 'label': '3456.oc.864.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '864.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935686
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': ['144.fg1', '144.fr1', '144.fs1', '144.ft1', '144.fm1', '144.fn1'], 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '12.v1', '12.y1'], 'contains': ['48.a1', '48.b1', '48.l1', '48.y1', '48.bw1', '72.cd1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38480884412, 2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.24.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': ['6.b1'], 'normal_contains': ['48.a1', '48.b1', '96.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '3456.oc', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935687
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.bc1', '288.bd1', '432.a1', '432.c1', '432.ba1', '432.be1', '432.be2', '432.bq1', '432.bu1', '432.by1', '432.bz1', '432.ca1', '432.ci1', '432.co1', '432.co2'], 'contains': ['1728.b1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1134693], 'label': '3456.oc.864.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '864.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935688
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.o1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.be1', '288.bf1', '432.g1', '432.w1', '432.ba1', '432.bm1', '432.bm2', '432.ck1', '432.cl1', '432.cm1', '432.cs1', '432.cs2'], 'contains': ['1728.b1', '1728.h1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1134693, 1968627499], 'label': '3456.oc.864.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935689
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.p1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bg1', '288.bh1', '432.h1', '432.x1', '432.be2', '432.be3', '432.bw1', '432.cb1', '432.cd1', '432.cm1', '432.cp1', '432.cs2'], 'contains': ['1728.b1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1134693, 1968627378], 'label': '3456.oc.864.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935690
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.p2', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bg2', '288.bh2', '432.h2', '432.x1', '432.be1', '432.be4', '432.bv1', '432.cc1', '432.ce1', '432.cf1', '432.cm1', '432.cp2', '432.cs1'], 'contains': ['1728.b1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1968627247, 1134693], 'label': '3456.oc.864.p2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.p2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.p2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935691
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.q1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.bi1', '288.bj1', '432.b1', '432.d1', '432.y1', '432.bc1', '432.bg1', '432.bh1', '432.bi1', '432.br1', '432.by1', '432.bz1', '432.cb1', '432.cc1', '432.cg1', '432.ct1', '432.cu1'], 'contains': ['1728.b1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 13414311772], 'label': '3456.oc.864.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '864.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935692
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.r1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bk1', '288.bl1', '432.c1', '432.u1', '432.bf1', '432.bo1', '432.bx1', '432.cg1', '432.ch1', '432.cl1', '432.cs1', '432.cs2'], 'contains': ['1728.b1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1967536007, 1134693], 'label': '3456.oc.864.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935693
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.s1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bm1', '288.bn1', '432.d1', '432.z1', '432.bg1', '432.bj1', '432.bp1', '432.bv1', '432.ca1', '432.cd1', '432.ch1', '432.cv1', '432.cw1'], 'contains': ['1728.b1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 1970078819], 'label': '3456.oc.864.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935694
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '864.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '12.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bo1', '288.bs1', '432.e1', '432.v1', '432.bh1', '432.bk1', '432.bs1', '432.by1', '432.cd1', '432.ce1', '432.ch1', '432.cq1', '432.cx1'], 'contains': ['1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1134693, 2951738], 'label': '3456.oc.864.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '864.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935695
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.u1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.bg1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.bp1', '288.bq1', '432.e1', '432.f1', '432.y1', '432.bd1', '432.bj1', '432.bk1', '432.bl1', '432.bt1', '432.bu1', '432.ca1', '432.cb1', '432.cf1', '432.cg1', '432.ct1', '432.cy1'], 'contains': ['1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13415036858, 1134693], 'label': '3456.oc.864.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '864.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935696
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.v1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.br1', '288.bt1', '432.f1', '432.z1', '432.bi1', '432.bl1', '432.bs1', '432.bw1', '432.bx1', '432.bz1', '432.ce1', '432.cv1', '432.cz1'], 'contains': ['1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 1970078440], 'label': '3456.oc.864.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '864.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935697
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '192.a1', 'complements': ['144.gy1', '144.t1', '144.gz1', '144.bj1', '144.bm1'], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.a1', '12.d1', '12.e1', '12.f1', '12.bu1', '12.by1', '12.cb1'], 'contains': ['72.a1', '72.b1', '72.gf1', '96.bd1', '96.bp1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.24.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.a1', '12.d1', '12.e1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
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id: 201935698
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '864.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.bu1', '288.bv1', '432.i1', '432.ci1', '432.cj1', '432.ck1', '432.cl1', '432.cm1', '432.cn1', '432.da1'], 'contains': ['1728.b1', '1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 2588323], 'label': '3456.oc.864.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '864.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935699
{'ambient': '3456.oc', 'aut_centralizer_order': 2304, 'aut_label': '864.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.bw1', '288.bx2', '432.j2', '432.co2', '432.cp2', '432.cr1', '432.cs2', '432.cu1', '432.cw1', '432.cx1', '432.cy1', '432.cz1', '432.da1'], 'contains': ['1728.b1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1863138, 2588323], 'label': '3456.oc.864.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '864.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.x1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935700
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.y1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.cb1', '288.cd1', '432.a1', '432.k1', '432.s1', '432.ci1', '432.cj1', '432.db1', '432.dc1', '432.dd2', '432.de1', '432.df1', '432.dj1'], 'contains': ['1728.c1', '1728.d1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 1862886], 'label': '3456.oc.864.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.y1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935701
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.z1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.cc1', '288.ce1', '432.i1', '432.l1', '432.s1', '432.t1', '432.cj1', '432.dd1', '432.de1', '432.df1', '432.dg1', '432.dh1', '432.dj1'], 'contains': ['1728.c1', '1728.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 13414673322], 'label': '3456.oc.864.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935702
{'ambient': '3456.oc', 'aut_centralizer_order': 768, 'aut_label': '864.ba1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cf1', '288.cg1', '432.q1', '432.u1', '432.ck1', '432.dc1', '432.dg1', '432.di1', '432.dk1'], 'contains': ['1728.c1', '1728.e1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1862886, 1967535360], 'label': '3456.oc.864.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935703
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '864.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.ch1', '288.ci1', '432.m1', '432.n1', '432.s1', '432.ci1', '432.db1', '432.dd1', '432.di1'], 'contains': ['1728.c1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13414673070, 1862886], 'label': '3456.oc.864.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '864.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bb1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935704
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.bc1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.cj1', '288.ck1', '432.k1', '432.u1', '432.w1', '432.cl1', '432.cm1', '432.dd1', '432.dd2', '432.dh1', '432.dl1'], 'contains': ['1728.c1', '1728.h1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1862886], 'label': '3456.oc.864.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bc1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935705
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.bd1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.cl1', '288.cm1', '432.l1', '432.w1', '432.x1', '432.ck1', '432.cm1', '432.db1', '432.de1', '432.dl1'], 'contains': ['1728.c1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1862886, 1969352442], 'label': '3456.oc.864.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bd1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935706
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.be1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cn1', '288.co1', '432.m1', '432.w1', '432.cl1', '432.df1', '432.dk1'], 'contains': ['1728.c1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1862886, 1969352190], 'label': '3456.oc.864.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.be1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935707
{'ambient': '3456.oc', 'aut_centralizer_order': 3456, 'aut_label': '864.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.cp1', '288.cq1', '288.cr1', '288.cs1', '288.ct1', '432.n1', '432.cn1', '432.dj1', '432.dk1', '432.dl1'], 'contains': ['1728.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2587950, 1862886], 'label': '3456.oc.864.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '864.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bf1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 201935708
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '24.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '288.958', 'aut_weyl_index': 144, 'centralizer': '24.c1', 'complements': ['144.u1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.c1', '12.bw1', '12.ca1', '12.cd1'], 'contains': ['48.cw1', '48.du1', '72.a1', '72.ge1'], 'core': '24.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.24.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': ['8.a1', '12.b1', '12.c1'], 'normal_contains': ['72.a1', '96.b1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '3456.oc', 'quotient_action_image': '24.14', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201935709
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.bg1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.cu1', '288.cy1', '432.b1', '432.o1', '432.bc1', '432.dm1', '432.dn1'], 'contains': ['1728.d1', '1728.f1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [2226652, 13413948127], 'label': '3456.oc.864.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '864.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bg1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935710
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '864.bh1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['288.cv1', '288.cz1', '432.g1', '432.l1', '432.ba1', '432.bb1', '432.be1', '432.be2', '432.be3', '432.be4', '432.bm1', '432.bm2', '432.db1', '432.dd1', '432.dd2', '432.de1'], 'contains': ['1728.d1', '1728.g1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13412085385, 1968627499], 'label': '3456.oc.864.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bh1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935711
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.bi1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.cw1', '288.da1', '432.c1', '432.k1', '432.ba1', '432.bf1', '432.bm1', '432.bm2', '432.dc1', '432.dd1', '432.df1'], 'contains': ['1728.d1', '1728.g1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13413948379], 'label': '3456.oc.864.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bi1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935712
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '864.bj1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.cx1', '288.db1', '432.d1', '432.o1', '432.bg1', '432.dm1', '432.dn1'], 'contains': ['1728.d1', '1728.i1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13413948379, 1970078819], 'label': '3456.oc.864.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bj1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935713
{'ambient': '3456.oc', 'aut_centralizer_order': 256, 'aut_label': '864.bk1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.dc1', '432.p1', '432.bb1', '432.bn1', '432.bn2', '432.dc1', '432.dg1', '432.dm1'], 'contains': ['1728.d1', '1728.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13413948127, 1967535360], 'label': '3456.oc.864.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bk1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935714
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.bl1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.dd1', '432.h1', '432.be4', '432.bm2', '432.bn1', '432.de1', '432.dh1'], 'contains': ['1728.d1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627499, 13414673322], 'label': '3456.oc.864.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bl1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935715
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.bl2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.dd2', '432.h2', '432.be3', '432.bm1', '432.bn2', '432.de1', '432.dh1', '432.dn1'], 'contains': ['1728.d1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1968627499, 13413219692], 'label': '3456.oc.864.bl2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '864.bl2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bl2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935716
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '864.bm1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['288.de1', '432.g1', '432.bf1', '432.bm1', '432.bm2', '432.bo1', '432.dd2', '432.df1', '432.dg1', '432.dh1'], 'contains': ['1728.d1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13413948127], 'label': '3456.oc.864.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bm1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935717
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.bn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.df1', '288.dh1', '288.di1', '432.r1', '432.bp1', '432.dm1'], 'contains': ['1728.e1', '1728.f1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2226652, 1967535360], 'label': '3456.oc.864.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bn1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935718
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '864.bo1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dj1', '432.q1', '432.bb1', '432.bq1', '432.dc1', '432.di1'], 'contains': ['1728.e1', '1728.g1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 1967535360], 'label': '3456.oc.864.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bo1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935719
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.c1', '8.b1', '12.s1'], 'contains': ['48.c1', '48.dd1', '48.dg1', '72.p1', '72.r1', '96.c1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 38480884412, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 201935720
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.bp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.dg1', '288.dk1', '432.r1', '432.br1', '432.dm1'], 'contains': ['1728.e1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13414311772, 1967535360], 'label': '3456.oc.864.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bp1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935721
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.bq1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.dl1', '288.dm1', '432.o1', '432.bp1', '432.bv1', '432.dn1'], 'contains': ['1728.f1', '1728.h1', '1728.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627247, 2226652], 'label': '3456.oc.864.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bq1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935722
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '864.br1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.dn1', '432.k1', '432.ba1', '432.be3', '432.be4', '432.bq1', '432.db1'], 'contains': ['1728.g1', '1728.h1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085767, 1968627499], 'label': '3456.oc.864.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.br1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935723
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '864.bs1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.do1', '432.m1', '432.ba1', '432.bf1', '432.dd2', '432.di1'], 'contains': ['1728.g1', '1728.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 13412085385], 'label': '3456.oc.864.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '864.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bs1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935724
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '864.bt1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['288.dp1', '432.o1', '432.br1', '432.cc1', '432.dn1'], 'contains': ['1728.h1', '1728.i1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627247, 13414311772], 'label': '3456.oc.864.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '864.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.bt1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935725
{'ambient': '3456.oc', 'aut_centralizer_order': 10368, 'aut_label': '1152.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '2.a1', 'complements': ['3.a1'], 'conjugacy_class_count': 2, 'contained_in': ['384.a1', '384.b1', '384.c1', '576.a1', '576.b1', '576.e1', '576.g1', '576.i1', '576.j1', '576.l1', '576.n1', '576.q1', '576.r1', '576.s1', '576.u1', '576.v1', '576.y1', '576.ba1'], 'contains': ['3456.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [38480520960], 'label': '3456.oc.1152.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1152.a1', 'normal_contained_in': ['288.a1', '384.a1', '576.a1'], 'normal_contains': ['3456.a1'], 'normalizer': '1.a1', 'old_label': '1152.a1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '576.8670', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '1152.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935726
{'ambient': '3456.oc', 'aut_centralizer_order': 10368, 'aut_label': '1152.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '4.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['384.a1', '384.d1', '384.e1', '576.f1', '576.h1', '576.m1', '576.o1', '576.t1', '576.z1', '576.bb1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37881446400], 'label': '3456.oc.1152.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '384.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '1152.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935727
{'ambient': '3456.oc', 'aut_centralizer_order': 1296, 'aut_label': '1152.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '32.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.by1', '288.cr1', '384.b1', '384.d1', '576.c1', '576.k1', '576.p1', '576.w1', '576.bc1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1137421], 'label': '3456.oc.1152.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '1152.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935728
{'ambient': '3456.oc', 'aut_centralizer_order': 324, 'aut_label': '1152.d1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['288.bz1', '288.cs1', '384.b1', '384.c1', '384.e1', '576.d1', '576.x1', '576.bd1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [38482336681], 'label': '3456.oc.1152.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1', 'old_label': '1152.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201935729
{'ambient': '3456.oc', 'aut_centralizer_order': 324, 'aut_label': '1152.e1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.ca1', '288.ct1', '384.c1', '384.d1', '384.e1', '576.be1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [37883665321], 'label': '3456.oc.1152.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.e1', 'old_label': '1152.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1152.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201935730
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.d1', '8.c1', '12.s1'], 'contains': ['48.c1', '48.dk1', '48.dl1', '72.s1', '72.t1', '72.u1', '96.d1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 38480884412, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935731
{'ambient': '3456.oc', 'aut_centralizer_order': 6912, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.a1', '576.b1', '576.c1', '576.d1', '864.b1', '864.c1', '864.d1', '864.e1', '864.f1', '864.g1', '864.h1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085120], 'label': '3456.oc.1728.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '1728.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935732
{'ambient': '3456.oc', 'aut_centralizer_order': 4608, 'aut_label': '1728.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['576.e1', '576.f1', '864.a1', '864.b1', '864.i1', '864.j1', '864.k1', '864.k2', '864.l1', '864.m1', '864.n1', '864.o1', '864.p1', '864.p2', '864.q1', '864.r1', '864.s1', '864.t1', '864.u1', '864.v1', '864.w1', '864.x1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1134693], 'label': '3456.oc.1728.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '1728.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935733
{'ambient': '3456.oc', 'aut_centralizer_order': 6912, 'aut_label': '1728.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.g1', '576.h1', '864.c1', '864.i1', '864.w1', '864.y1', '864.z1', '864.ba1', '864.bb1', '864.bc1', '864.bd1', '864.be1', '864.bf1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1862886], 'label': '3456.oc.1728.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '1728.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935734
{'ambient': '3456.oc', 'aut_centralizer_order': 768, 'aut_label': '1728.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['576.i1', '576.j1', '864.b1', '864.d1', '864.j1', '864.k1', '864.k2', '864.y1', '864.z1', '864.bg1', '864.bh1', '864.bi1', '864.bj1', '864.bk1', '864.bl1', '864.bl2', '864.bm1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948127], 'label': '3456.oc.1728.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '1728.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935735
{'ambient': '3456.oc', 'aut_centralizer_order': 4608, 'aut_label': '1728.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.k1', '576.l1', '576.m1', '864.h1', '864.l1', '864.ba1', '864.bk1', '864.bn1', '864.bo1', '864.bp1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967535360], 'label': '3456.oc.1728.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '1728.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935736
{'ambient': '3456.oc', 'aut_centralizer_order': 3456, 'aut_label': '1728.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '12.w1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.n1', '576.o1', '576.p1', '864.e1', '864.m1', '864.bg1', '864.bn1', '864.bq1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2226652], 'label': '3456.oc.1728.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '1728.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935737
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '1728.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.q1', '576.r1', '864.c1', '864.f1', '864.j1', '864.n1', '864.y1', '864.bb1', '864.bh1', '864.bi1', '864.bo1', '864.br1', '864.bs1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085385], 'label': '3456.oc.1728.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '1728.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935738
{'ambient': '3456.oc', 'aut_centralizer_order': 512, 'aut_label': '1728.h1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '27.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['576.s1', '576.t1', '864.d1', '864.l1', '864.o1', '864.p1', '864.p2', '864.bc1', '864.bd1', '864.bh1', '864.bl1', '864.bl2', '864.bq1', '864.br1', '864.bt1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1968627499], 'label': '3456.oc.1728.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '1728.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201935739
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '1728.i1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['576.u1', '576.v1', '576.w1', '576.x1', '864.e1', '864.g1', '864.q1', '864.bg1', '864.bj1', '864.bp1', '864.bt1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13414311772], 'label': '3456.oc.1728.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '1728.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935740
{'ambient': '3456.oc', 'aut_centralizer_order': 768, 'aut_label': '1728.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.y1', '576.z1', '864.f1', '864.o1', '864.r1', '864.ba1', '864.bc1', '864.be1', '864.bi1', '864.bm1', '864.bs1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007], 'label': '3456.oc.1728.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '1728.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935741
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.m1', '12.t1'], 'contains': ['48.e1', '48.f1', '48.i1', '48.be1', '48.bh1', '48.cd1', '48.ch1', '72.c1', '72.bd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 265, 13412085385, 38481612847, 1862886, 2226652], 'label': '3456.oc.24.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935742
{'ambient': '3456.oc', 'aut_centralizer_order': 384, 'aut_label': '1728.k1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.ba1', '576.bb1', '576.bc1', '576.bd1', '576.be1', '864.g1', '864.s1', '864.bj1', '864.bn1', '864.bq1'], 'contains': ['3456.a1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1970078819], 'label': '3456.oc.1728.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.p1', 'old_label': '1728.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935743
{'ambient': '3456.oc', 'aut_centralizer_order': None, 'aut_label': '3456.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1152.a1', '1152.b1', '1152.c1', '1152.d1', '1152.e1', '1728.a1', '1728.b1', '1728.c1', '1728.d1', '1728.e1', '1728.f1', '1728.g1', '1728.h1', '1728.i1', '1728.j1', '1728.k1'], 'contains': [], 'core': '3456.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '3456.oc.3456.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3456.a1', 'normal_contained_in': ['864.a1', '1152.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '3456.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3456.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201935744
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.n1', '12.t1'], 'contains': ['48.e1', '48.h1', '48.j1', '48.bh1', '48.bi1', '48.ci1', '48.cj1', '72.d1', '72.be1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602744206, 1134054, 1968991665, 38480884412, 13413219692, 526], 'label': '3456.oc.24.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935762
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.i1', '8.c1'], 'contains': ['48.o1', '48.dh1', '48.dm1', '72.u1', '72.bs1', '96.l1'], 'core': '144.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39799592563, 604926858, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '24.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935745
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.q1', '12.u1'], 'contains': ['48.e1', '48.k1', '48.q1', '48.r1', '48.s1', '48.bb1', '48.bf1', '48.bj1', '48.dv1', '48.dx1', '48.dz1', '72.e1', '72.bf1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 13412085385, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.24.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935746
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '8.f1', '8.g1', '12.s1', '12.v1', '16.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1967901282, 1863007, 2226652, 2586614, 604203487, 13413948127, 2588323, 38480884412], 'label': '3456.oc.4.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '4.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201935747
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.h1', '12.y1'], 'contains': ['48.e1', '48.l1', '48.l2', '48.r1', '48.bc1', '48.bg1', '48.bn1', '48.bn2', '48.dy1', '72.f1', '72.bg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1969352563, 526, 1862886, 13414673191, 38481612978, 604203618], 'label': '3456.oc.24.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935748
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.j1', '12.t1'], 'contains': ['48.f1', '48.g1', '48.j1', '48.cd1', '48.cg1', '48.ci1', '48.cp1', '72.g1', '72.bh1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 602743680, 1967536007, 1134693, 2226652, 38480884533], 'label': '3456.oc.24.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935749
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.k1', '12.t1'], 'contains': ['48.g1', '48.h1', '48.i1', '48.ch1', '48.cj1', '48.cp1', '48.cq1', '72.h1', '72.bi1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 602743680, 1967536007, 1134693, 2951738, 38480884533], 'label': '3456.oc.24.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935750
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.j1', '12.v1'], 'contains': ['48.f1', '48.j1', '48.l1', '48.bm1', '48.br1', '48.cf1', '48.ck1', '72.i1', '72.bj1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 1968627378, 38480884533, 13412085120], 'label': '3456.oc.24.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935751
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.i1', '12.w1'], 'contains': ['48.f1', '48.h1', '48.l2', '48.w1', '48.bl1', '48.bp1', '48.ce1', '48.cl1', '48.ej1', '72.j1', '72.bk1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 2226652, 38480884533, 13412085120], 'label': '3456.oc.24.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935752
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.k1', '12.v1'], 'contains': ['48.h1', '48.i1', '48.l1', '48.bq1', '48.bs1', '48.ck1', '48.cm1', '72.k1', '72.bl1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 1968627378, 38480884533, 13412085120], 'label': '3456.oc.24.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935753
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.i1', '12.x1'], 'contains': ['48.i1', '48.j1', '48.l2', '48.bt1', '48.bu1', '48.cn1', '48.co1', '72.l1', '72.bm1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 2951738, 38480884533, 13412085120], 'label': '3456.oc.24.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935754
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.u1'], 'contains': ['48.g1', '48.k1', '48.m1', '48.q1', '48.s1', '48.bj1', '48.bo1', '48.cr1', '48.cu1', '48.dx2', '48.dz1', '72.m1', '72.bn1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1967536007, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.24.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935755
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.h1', '12.q1', '12.y1'], 'contains': ['48.k1', '48.l1', '48.l2', '48.m1', '48.q1', '48.r1', '48.bn3', '48.bn4', '48.bv1', '48.bv2', '48.cs1', '48.cv1', '48.dy1', '48.eb1', '72.n1', '72.bo1'], 'core': '192.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967535625, 1862886, 2588323, 38480884533, 13412085120, 604203366], 'label': '3456.oc.24.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935756
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.h1', '12.u1'], 'contains': ['48.e1', '48.m1', '48.v1', '48.bb1', '48.cr1', '48.cw1', '48.ed1', '72.o1', '72.bp1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13412085646, 2587950, 38480884412, 526, 1862886, 604203618], 'label': '3456.oc.24.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201935757
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '576.a1', 'complements': ['576.l1', '576.s1', '576.y1', '576.m1', '576.t1', '576.z1', '576.a1', '576.j1', '576.r1', '576.ba1', '576.bb1', '576.v1', '576.bd1', '576.be1', '576.x1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.d1', '12.e1', '18.d1', '18.k1', '24.u1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [39799592190, 13412085385, 1862886, 2951738, 647, 526, 2588323, 1137421], 'label': '3456.oc.6.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '12.d1', '12.e1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201935758
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.b1', '12.i1', '12.m1', '12.v1'], 'contains': ['48.a1', '48.f1', '48.i1', '48.bm1', '48.bq1', '48.db1', '48.di1', '72.p1', '72.bq1'], 'core': '48.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 38480884412, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935759
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.j1', '12.m1', '12.w1'], 'contains': ['48.f1', '48.p1', '48.bl1', '48.dc1', '48.dj1', '72.q1', '72.br1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2226652, 1863007, 13413948127], 'label': '3456.oc.24.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935760
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.a1', '8.b1', '12.s1'], 'contains': ['48.n1', '48.dd1', '48.dk1', '72.r1', '72.bq1', '96.i1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39799592563, 1137421, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '24.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 201935761
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.h1', '8.c1', '12.s1'], 'contains': ['48.n1', '48.dg1', '48.dl1', '72.t1', '72.bs1', '96.k1'], 'core': '144.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39799592563, 1137421, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 201935763
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '12.i1', '12.n1', '12.v1'], 'contains': ['48.a1', '48.h1', '48.j1', '48.br1', '48.bs1', '48.di1', '48.dn1', '72.s1', '72.bs1'], 'core': '48.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 38480884412, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.24.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935764
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 48, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.k1', '12.n1', '12.w1'], 'contains': ['48.h1', '48.p1', '48.bp1', '48.dj1', '48.dq1', '72.v1', '72.bt1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2588071, 1969714258, 1863259, 604928551, 13413219692, 38480884412], 'label': '3456.oc.24.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935765
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.k1', '12.l1', '12.m1', '12.o1', '12.x1'], 'contains': ['48.i1', '48.p1', '48.bt1', '48.dr1', '48.ds1', '72.w1', '72.bu1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2951738, 1863007, 13413948127], 'label': '3456.oc.24.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935766
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.958', 'aut_weyl_index': 144, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.l1', '12.n1', '12.p1', '12.x1'], 'contains': ['48.j1', '48.p1', '48.bu1', '48.ds1', '48.dt1', '72.x1', '72.bv1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604928551, 1863259, 38480884412, 2588071, 1968991665, 13413219692], 'label': '3456.oc.24.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935767
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.q1', '12.y1'], 'contains': ['48.a1', '48.g1', '48.k1', '48.l2', '48.bn1', '48.bv1', '48.bx1', '48.cx1', '48.df1', '72.y1', '72.bw1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 13413948258, 1967536007, 38480884412, 2588323, 1863007], 'label': '3456.oc.24.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935768
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2592.fs', 'aut_weyl_index': 16, 'centralizer': '216.a1', 'complements': ['576.p1', '576.bc1', '576.bd1', '576.be1', '576.w1', '576.x1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.b1', '12.c1', '12.h1', '12.q1', '12.u1', '12.y1', '12.ba1', '12.bm1', '18.o1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1967536007, 13412085385, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.6.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['12.b1', '12.c1', '24.a1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '3456.oc', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935769
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bb2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.k1', '12.l1', '12.q1', '12.y1'], 'contains': ['48.g1', '48.k1', '48.l1', '48.p1', '48.bn2', '48.bv2', '48.bx1', '48.cx2', '48.df2', '72.y2', '72.bw2'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 1967536007, 1863138, 2588323, 13413948127, 604203618], 'label': '3456.oc.24.bb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bb2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935770
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.b1', '12.m1', '12.n1', '12.o1', '12.p1', '12.q1', '12.y1'], 'contains': ['48.a1', '48.e1', '48.m1', '48.p1', '48.bc1', '48.cs1', '48.cx1', '48.cx2', '48.du1', '72.z1', '72.bx1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085646, 38480884129, 526, 1862886, 2588323, 604203618], 'label': '3456.oc.24.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201935771
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.u1'], 'contains': ['48.q1', '48.r1', '48.v1', '48.dv1', '48.dx2', '48.ed1', '48.eh1', '72.ba1', '72.by1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13412085767, 2587950, 1967536007, 38480883894, 1862886, 604203366], 'label': '3456.oc.24.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935772
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.k1', '8.d1', '12.s1'], 'contains': ['48.c1', '48.n1', '48.cy1', '72.bb1', '72.cd1', '96.n1'], 'core': '144.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967901282, 1863007, 2586614, 38480884412, 13413948127, 2588323], 'label': '3456.oc.24.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 201935773
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.k1', '8.e1'], 'contains': ['48.d1', '48.t1', '48.ee1', '72.bc1', '72.ce1', '96.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1967901282, 1862886, 1137042], 'label': '3456.oc.24.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bf1', 'old_label': '24.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
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id: 201935774
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.u1', '12.y1'], 'contains': ['48.e1', '48.g1', '48.q1', '48.y1', '48.z1', '48.bd1', '48.bz1', '48.dw1', '72.bz1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 38481612978, 1967535360, 604203618], 'label': '3456.oc.24.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935775
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.v1', '12.w1'], 'contains': ['48.f1', '48.h1', '48.w1', '48.y1', '48.ba1', '48.by1', '48.ca1', '48.ei1', '72.ca1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.24.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935776
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.v1', '12.x1'], 'contains': ['48.i1', '48.j1', '48.y1', '48.cb1', '48.cc1', '72.cb1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.24.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935777
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.u1', '12.y1'], 'contains': ['48.k1', '48.m1', '48.r1', '48.y1', '48.z1', '48.bk1', '48.ct1', '48.ea1', '72.cc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 1967535360, 13412085120, 2588323, 604203366, 38480884533], 'label': '3456.oc.24.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935778
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '12.x1', '12.y1'], 'contains': ['48.l2', '48.p1', '48.y1', '48.bw2', '48.da1', '72.cd2'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [38480884129, 13413948258, 1863138, 2588323, 604203618, 1967535360], 'label': '3456.oc.24.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935779
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.d1', '12.f1', '12.by1', '18.c1', '18.d1', '24.d1'], 'core': '12.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085385, 1862886, 2951738, 647, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.6.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201935780
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '12.u1'], 'contains': ['48.s1', '48.v1', '48.z1', '48.ec1', '48.eg1', '72.ce1'], 'core': '96.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1862886, 1969352190, 604203366], 'label': '3456.oc.24.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '24.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
-
id: 201935781
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.u1', '12.ba1', '12.bm1'], 'contains': ['48.bb1', '48.bd1', '48.bk1', '48.bo1', '48.dw1', '48.dx1', '48.dx2', '48.ea1', '48.ec1', '72.ch1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [526, 1862886, 38481612978, 1967535360, 13414673322, 604203618], 'label': '3456.oc.24.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935782
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.230', 'aut_weyl_index': 432, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.m1', '12.z1'], 'contains': ['48.bc1', '48.be1', '48.bh1', '48.bl1', '48.bm1', '48.bq1', '48.bt1', '72.cf1', '72.ck1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 1862886, 2226652, 13414673322], 'label': '3456.oc.24.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935783
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.h1', '12.bm1'], 'contains': ['48.bb1', '48.bg1', '48.bn3', '48.bn4', '48.dv1', '48.dy1', '72.ci1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1969352563, 13412085385, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.24.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935784
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.n1', '12.z1'], 'contains': ['48.bc1', '48.bh1', '48.bi1', '48.bp1', '48.br1', '48.bs1', '48.bu1', '72.cg1', '72.cl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38480884412, 526, 1968991665, 1134054, 602744206, 13413948127], 'label': '3456.oc.24.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935785
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.q1', '12.ba1'], 'contains': ['48.bb1', '48.bc1', '48.bf1', '48.bv1', '48.bv2', '48.dx2', '48.dy1', '48.dz1', '48.eb1', '72.cj1', '72.cm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 38481612978, 604203618, 13414673322], 'label': '3456.oc.24.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935786
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.y1', '12.z1', '12.ba1'], 'contains': ['48.bc1', '48.bd1', '48.bw1', '48.bw2', '48.bx1', '48.ea1', '48.eb1', '72.cn1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [526, 1862886, 13414673191, 38481612978, 604203618, 1967535360], 'label': '3456.oc.24.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935787
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.z1', '12.bn1'], 'contains': ['48.bd1', '48.be1', '48.bi1', '48.by1', '48.cb1', '48.cg1', '48.cq1', '72.co1', '72.cp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 1862886, 2226652, 1967535360], 'label': '3456.oc.24.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935788
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.z1', '12.bo1'], 'contains': ['48.bd1', '48.bh1', '48.ca1', '48.cc1', '48.cp1', '72.cq1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 13413586612, 1862886, 1967535360], 'label': '3456.oc.24.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935789
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.bn1'], 'contains': ['48.be1', '48.bg1', '48.bi1', '48.ce1', '48.cf1', '48.cm1', '48.cn1', '72.cr1', '72.cs1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 1969352563, 265, 38481612847, 1862886, 2226652], 'label': '3456.oc.24.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935790
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.e1', '12.f1', '12.cb1', '18.e1', '18.f1', '18.g1', '24.e1'], 'core': '12.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 13412085385, 38480884412, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.6.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201935791
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.bo1'], 'contains': ['48.bg1', '48.bh1', '48.ck1', '48.cl1', '48.co1', '72.ct1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 1969352563, 265, 38481612847, 13413586612, 1862886], 'label': '3456.oc.24.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935792
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.j1', '12.bb1'], 'contains': ['48.bl1', '48.bn2', '48.bu1', '48.cd1', '48.cf1', '48.ci1', '48.ck1', '72.cu1', '72.cy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 13413948127, 1968627378, 38480884533], 'label': '3456.oc.24.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935793
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.i1', '12.bc1'], 'contains': ['48.bm1', '48.bn1', '48.bs1', '48.cd1', '48.ce1', '48.cj1', '48.co1', '72.cv1', '72.cz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 602743680, 1968627247, 1134693, 2226652, 38480884533], 'label': '3456.oc.24.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935794
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.k1', '12.bb1'], 'contains': ['48.bn2', '48.bp1', '48.bt1', '48.ch1', '48.cj1', '48.ck1', '48.cm1', '72.cw1', '72.da1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 13413948127, 1968627378, 38480884533], 'label': '3456.oc.24.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935795
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '12.i1', '12.bd1'], 'contains': ['48.bn1', '48.bq1', '48.br1', '48.ch1', '48.ci1', '48.cl1', '48.cn1', '72.cx1', '72.db1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 602743680, 1968627247, 1134693, 2951738, 38480884533], 'label': '3456.oc.24.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935796
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.w1', '12.z1', '12.bb1'], 'contains': ['48.bl1', '48.bp1', '48.bw2', '48.by1', '48.ca1', '48.ei1', '48.ej1', '72.dc1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 1967535360, 13413948127, 38480884533], 'label': '3456.oc.24.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935797
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.v1', '12.z1', '12.bc1'], 'contains': ['48.bm1', '48.bs1', '48.bw1', '48.by1', '48.cc1', '72.dd1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.24.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935798
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.v1', '12.z1', '12.bd1'], 'contains': ['48.bq1', '48.br1', '48.bw1', '48.ca1', '48.cb1', '72.de1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.24.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935799
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.x1', '12.z1', '12.bb1'], 'contains': ['48.bt1', '48.bu1', '48.bw2', '48.cb1', '48.cc1', '72.df1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 13413948127, 1967535360, 38480884533], 'label': '3456.oc.24.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935800
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.j1', '12.z1'], 'contains': ['48.bl1', '48.bm1', '48.br1', '48.bu1', '48.bx1', '48.cg1', '48.cp1', '72.dg1', '72.dh1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 2226652, 13413948127, 38480884533], 'label': '3456.oc.24.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935801
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.b1'], 'contains': ['12.j1', '12.l1', '12.m1', '12.p1', '12.q1', '12.bf1', '12.bg1', '12.bi1', '12.bk1', '12.br1', '12.bs1', '18.a1', '18.i1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 13412085385, 526, 602744206, 2951391], 'label': '3456.oc.6.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935802
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.k1', '12.z1'], 'contains': ['48.bp1', '48.bq1', '48.bs1', '48.bt1', '48.bx1', '48.cp1', '48.cq1', '72.di1', '72.dj1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 2951738, 13413948127, 38480884533], 'label': '3456.oc.24.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935803
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.bb1', '12.bc1'], 'contains': ['48.by1', '48.bz1', '48.cc1', '48.cd1', '48.cj1', '72.dk1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.24.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935804
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.t1', '12.bb1', '12.bd1'], 'contains': ['48.bz1', '48.ca1', '48.cb1', '48.ch1', '48.ci1', '72.dl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.24.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935805
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.u1', '12.bm1'], 'contains': ['48.bj1', '48.bk1', '48.bz1', '48.cr1', '48.ct1', '48.dv1', '48.dw1', '48.ec1', '72.dm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323, 1967535360, 38480884533, 604203366], 'label': '3456.oc.24.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935806
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.h1', '12.q1', '12.bm1'], 'contains': ['48.bj1', '48.bn1', '48.bn2', '48.bn3', '48.bn4', '48.bv1', '48.bv2', '48.cr1', '48.cs1', '48.cv1', '48.dv1', '48.dx1', '48.dx2', '48.dy1', '72.dn1', '72.do1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13412085646, 1967535625, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.24.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935807
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.y1', '12.ba1', '12.bm1'], 'contains': ['48.bk1', '48.bv1', '48.bv2', '48.bw1', '48.bw2', '48.cs1', '48.ct1', '48.dw1', '48.dy1', '48.ea1', '72.dp1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 1862886, 2588323, 1967535360, 38480884533, 604203366], 'label': '3456.oc.24.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935808
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.ba1'], 'contains': ['48.bo1', '48.bv1', '48.bv2', '48.bx1', '48.cs1', '48.cu1', '48.dx1', '48.dz1', '48.eb1', '72.dq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 13412085385, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.24.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cl1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935809
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '24.cm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.h1', '12.ba1'], 'contains': ['48.bb1', '48.bc1', '48.cs1', '48.cw1', '48.ed1', '72.dr1', '72.ds1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 13412085385, 38480884412, 526, 1862886, 604203618], 'label': '3456.oc.24.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201935810
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.u1', '12.ba1'], 'contains': ['48.bd1', '48.bf1', '48.ct1', '48.cu1', '48.cw1', '48.eg1', '48.eh1', '72.dt1', '72.du1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 38480884412, 526, 1862886, 604203618, 1967535360], 'label': '3456.oc.24.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935811
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.h1'], 'contains': ['48.bf1', '48.bg1', '48.cv1', '48.cw1', '48.eh1', '72.dv1', '72.dw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 1967536007, 38480884412, 526, 1862886, 604203618], 'label': '3456.oc.24.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.co1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935812
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6912.ed', 'aut_weyl_index': 6, 'centralizer': '1152.a1', 'complements': ['1728.e1', '1728.h1', '1728.j1', '1728.a1', '1728.d1', '1728.g1', '1728.k1', '1728.i1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '6.a1', '6.c1', '6.g1', '8.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [526, 647, 38480884412, 2588323, 2951738, 1137421, 13412085385, 1862886, 604203618], 'label': '3456.oc.2.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157864'}
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id: 201935813
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.b1'], 'contains': ['12.k1', '12.l1', '12.n1', '12.o1', '12.q1', '12.bg1', '12.bh1', '12.bj1', '12.bl1', '12.bs1', '12.bt1', '18.b1', '18.j1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 2951738, 13412085385, 526, 602744206], 'label': '3456.oc.6.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201935814
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.cp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.230', 'aut_weyl_index': 432, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.m1', '12.bb1'], 'contains': ['48.bl1', '48.bt1', '48.cd1', '48.ch1', '48.cx1', '48.db1', '48.di1', '72.dx1', '72.ef1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 13412085385, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.24.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935815
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.cq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.m1', '12.bc1', '12.bf1', '12.bi1'], 'contains': ['48.bm1', '48.cd1', '48.cx2', '48.dc1', '48.ds1', '72.dy1', '72.eg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 13412085385, 2226652, 1863007], 'label': '3456.oc.24.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cq1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 201935816
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.cr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '12.n1', '12.bb1'], 'contains': ['48.bp1', '48.bu1', '48.ci1', '48.cj1', '48.cx1', '48.di1', '48.dn1', '72.ea1', '72.eh1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 604203487, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.24.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cr1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201935817
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.cs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.k1', '12.m1', '12.bd1', '12.bg1', '12.bj1'], 'contains': ['48.bq1', '48.ch1', '48.cx2', '48.dj1', '48.dr1', '72.dz1', '72.ej1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 13412085385, 2226275, 1863007], 'label': '3456.oc.24.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cs1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 201935818
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.n1', '12.bd1', '12.bg1', '12.bk1'], 'contains': ['48.br1', '48.ci1', '48.cx2', '48.dj1', '48.dt1', '72.eb1', '72.ei1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604928551, 1863259, 1968991316, 13412085385, 38480884412, 2588071], 'label': '3456.oc.24.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ct1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201935819
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.cu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.k1', '12.n1', '12.bc1', '12.bh1', '12.bl1'], 'contains': ['48.bs1', '48.cj1', '48.cx2', '48.dq1', '48.ds1', '72.ec1', '72.ek1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085385, 2588071, 1969714258, 1863259, 604928551, 38480884412], 'label': '3456.oc.24.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cu1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201935820
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.cv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '96.230', 'aut_weyl_index': 432, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.l1', '12.o1', '12.be1', '12.bg1', '12.bh1', '12.bi1', '12.bj1'], 'contains': ['48.cx2', '48.dr1', '48.ds1', '72.ed1', '72.el1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2951738, 13412085385, 1863007], 'label': '3456.oc.24.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cv1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 201935821
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.cw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.l1', '12.p1', '12.be1', '12.bf1', '12.bg1', '12.bk1', '12.bl1'], 'contains': ['48.cx2', '48.ds1', '48.dt1', '72.ee1', '72.em1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604928551, 1863259, 13412085385, 38480884412, 2588071, 1968991665], 'label': '3456.oc.24.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cw1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201935822
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cx1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.y1', '12.bb1', '12.bm1'], 'contains': ['48.b1', '48.bk1', '48.bn2', '48.bn3', '48.bw2', '48.bz1', '48.cx1', '72.en1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 604203487, 38480884412, 2588323, 1863007, 1967535360], 'label': '3456.oc.24.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935823
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cx2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.y1', '12.bc1', '12.bd1', '12.be1', '12.bm1'], 'contains': ['48.bk1', '48.bn1', '48.bn4', '48.bw1', '48.bz1', '48.cx2', '48.da1', '72.en2'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 38480884129, 1863138, 2588323, 604203618, 1967535360], 'label': '3456.oc.24.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cx2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cx2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935824
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 72, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.b1', '12.m1', '12.o1', '12.bi1', '12.bj1', '12.bw1', '12.ca1', '18.c1', '18.k1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085385, 1862886, 2951738, 647, 38480884412, 2588323, 526, 604203618], 'label': '3456.oc.6.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 201935825
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cy1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '12.bf1', '12.bg1', '12.bh1', '12.bm1'], 'contains': ['48.bj1', '48.bn3', '48.bo1', '48.bv1', '48.cx2', '48.df2', '72.eo1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 1967536007, 13412085385, 1863138, 2588323, 604203618], 'label': '3456.oc.24.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935826
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.cy2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.q1', '12.bm1'], 'contains': ['48.bj1', '48.bn4', '48.bo1', '48.bv2', '48.cx1', '48.df1', '72.eo2'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 1967536007, 13412085385, 38480884412, 2588323, 1863007], 'label': '3456.oc.24.cy2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.cy2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cy2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935827
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.cz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.p1', '8.f1', '12.s1'], 'contains': ['48.cy1', '48.dd1', '48.dl1', '72.ep1', '72.er1', '96.cb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967901282, 1863007, 2226652, 2586614, 38480884412, 2588323], 'label': '3456.oc.24.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935828
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.da1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.q1', '8.f1'], 'contains': ['48.cz1', '48.de1', '48.do1', '72.ep1', '72.es1', '96.cc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [37882213052, 2586614, 1967901282, 2226652, 2588323, 1863007], 'label': '3456.oc.24.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1', 'old_label': '24.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.da1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935829
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.db1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.r1', '8.g1', '12.s1'], 'contains': ['48.cy1', '48.dg1', '48.dk1', '72.eq1', '72.ev1', '96.cd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2586735, 38480884412, 13413586612, 1967901775, 2588323, 1863007], 'label': '3456.oc.24.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '24.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.db1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 201935830
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.dc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.f1', '12.v1', '12.bb1', '12.bn1'], 'contains': ['48.b1', '48.by1', '48.cb1', '48.cf1', '48.cm1', '48.db1', '48.dn1', '72.er1', '72.es1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38480884412, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.24.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dc1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935831
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.dd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '12.bc1', '12.bn1'], 'contains': ['48.by1', '48.ce1', '48.da1', '48.dc1', '48.dq1', '72.et1', '72.eu1'], 'core': '192.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2226652, 1863007, 1967535360], 'label': '3456.oc.24.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dd1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935832
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.de1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.g1', '12.v1', '12.bb1', '12.bo1'], 'contains': ['48.b1', '48.ca1', '48.cc1', '48.ck1', '48.di1', '72.ev1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38480884412, 13413586612, 2588323, 1863007, 1967535360], 'label': '3456.oc.24.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.de1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935833
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.df1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1', '12.bd1', '12.bo1'], 'contains': ['48.ca1', '48.cl1', '48.da1', '48.dj1', '72.ew1'], 'core': '192.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [13413586379, 604203487, 38482338042, 2588202, 1863007, 1967535360], 'label': '3456.oc.24.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.df1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935834
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.dg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8399', 'aut_weyl_index': 72, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.x1', '12.bd1', '12.be1', '12.bn1', '12.bp1'], 'contains': ['48.cb1', '48.cn1', '48.da1', '48.dr1', '48.dt1', '72.ex1', '72.ez1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1863007, 2951391, 1967535360], 'label': '3456.oc.24.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935835
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.by1', '12.cb1', '18.f1', '18.l1', '24.v1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 13412085385, 39799592190, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.6.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201935836
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '24.dh1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8399', 'aut_weyl_index': 72, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.x1', '12.bc1', '12.be1', '12.bo1', '12.bq1'], 'contains': ['48.cc1', '48.co1', '48.da1', '48.ds1', '72.ey1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 13413586612, 1863007, 1967535360], 'label': '3456.oc.24.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dh1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935837
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.di1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.i1', '12.bn1'], 'contains': ['48.ce1', '48.cg1', '48.cn1', '48.cq1', '48.db1', '48.df1', '48.dn1', '72.fa1', '72.fb1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1968627126, 604203487, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.24.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.di1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935838
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dj1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.j1', '12.bf1', '12.bn1', '12.br1'], 'contains': ['48.cf1', '48.cg1', '48.dc1', '48.df2', '48.dt1', '72.fc1', '72.fd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.24.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dj1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935839
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.i1', '12.bo1'], 'contains': ['48.cl1', '48.co1', '48.cp1', '48.df1', '48.di1', '72.ff1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1968627126, 604203487, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.24.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '24.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935840
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dk2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '12.k1', '12.bg1', '12.bo1', '12.bs1'], 'contains': ['48.ck1', '48.cp1', '48.df2', '48.dj1', '48.ds1', '72.fe1', '72.fg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413586379, 604203487, 38482338042, 2588202, 1967536007, 1863007], 'label': '3456.oc.24.dk2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dk2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dk2', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935841
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dl1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.k1', '12.bh1', '12.bn1', '12.bt1'], 'contains': ['48.cm1', '48.cq1', '48.df2', '48.dq1', '48.dr1', '72.fh1', '72.fi1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.24.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935842
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.l1', '12.bg1', '12.bp1', '12.br1', '12.bt1'], 'contains': ['48.df2', '48.dr1', '48.dt1', '72.fj1', '72.fl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 2226275, 1863007], 'label': '3456.oc.24.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dm1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935843
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.l1', '12.bf1', '12.bh1', '12.bq1', '12.bs1'], 'contains': ['48.df2', '48.ds1', '72.fk1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 1863007, 13415398178], 'label': '3456.oc.24.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935844
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '24.do1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.b1', '12.q1', '12.bi1', '12.bj1', '12.bk1', '12.bl1', '12.bm1'], 'contains': ['48.bb1', '48.cr1', '48.cs1', '48.cx1', '48.cx2', '48.du1', '72.fm1', '72.fn1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 13412085385, 526, 1862886, 2588323, 604203618], 'label': '3456.oc.24.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.do1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.do1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935845
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.dp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.y1', '12.bm1', '12.bn1', '12.bo1', '12.bp1', '12.bq1'], 'contains': ['48.b1', '48.bd1', '48.bg1', '48.ct1', '48.cv1', '48.da1', '48.df1', '48.df2', '48.du1', '72.fo1', '72.fp1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [38480884129, 526, 1862886, 2588323, 604203618, 1967535360], 'label': '3456.oc.24.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935846
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['12.r1', '12.bz1', '12.cc1', '18.g1', '18.l1', '24.w1'], 'core': '36.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39799592190, 13412085385, 1862886, 604926858, 647, 1968991665, 526, 2588323], 'label': '3456.oc.6.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '6.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201935847
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '24.dq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 324, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.m1', '12.bi1', '12.bn1', '12.br1', '12.bw1'], 'contains': ['48.be1', '48.db1', '48.dc1', '48.dr1', '48.du1', '72.fq1', '72.fr1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 602744206, 2951391], 'label': '3456.oc.24.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dq1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 201935848
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.dr1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.q1', '12.br1', '12.bs1', '12.bt1'], 'contains': ['48.bf1', '48.cu1', '48.cv1', '48.df1', '48.df2', '48.du1', '72.fs1', '72.ft1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [38480884129, 1967536007, 526, 1862886, 2588323, 604203618], 'label': '3456.oc.24.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dr1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935849
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.ds1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.m1', '12.n1', '12.bj1', '12.bk1', '12.bo1', '12.bs1', '12.ca1'], 'contains': ['48.bh1', '48.di1', '48.dj1', '48.ds1', '48.du1', '72.fu1', '72.fv1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 13415398178, 602744206], 'label': '3456.oc.24.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.ds1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ds1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201935850
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.n1', '12.bl1', '12.bn1', '12.bt1', '12.cd1'], 'contains': ['48.bi1', '48.dn1', '48.dq1', '48.dt1', '48.du1', '72.fw1', '72.fx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38480884412, 526, 1968991665, 2588323, 602744206], 'label': '3456.oc.24.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dt1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935851
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '24.du1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 324, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.o1', '12.bj1', '12.bp1', '12.bt1', '12.bw1'], 'contains': ['48.dr1', '48.du1', '72.fy1', '72.gc1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 526, 602744206], 'label': '3456.oc.24.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.du1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.du1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
-
id: 201935852
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '24.dv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '12.p1', '12.bi1', '12.bl1', '12.bq1', '12.bs1', '12.ca1'], 'contains': ['48.ds1', '48.du1', '72.fz1', '72.ga1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 602744206, 13415397945], 'label': '3456.oc.24.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dv1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201935853
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '24.dw1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.p1', '12.bk1', '12.bp1', '12.br1', '12.cd1'], 'contains': ['48.dt1', '48.du1', '72.gb1', '72.gd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 1968991316, 38480884412, 526, 2588323, 602744206], 'label': '3456.oc.24.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '24.dw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dw1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935854
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '24.dx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.r1', '12.bz1', '12.cc1'], 'contains': ['72.a1', '72.gf1', '72.gg1', '96.be1', '96.bq1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [604926858, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.24.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '24.dx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dx1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201935855
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '24.dy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.bv1', '12.bx1', '12.ce1'], 'contains': ['72.b1', '72.ge1', '72.gg1', '96.bg1', '96.bs1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37882213052, 1137421, 526, 647, 1862886, 2588323], 'label': '3456.oc.24.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '24.dy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dy1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201935856
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '24.dz1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.cf1'], 'contains': ['72.ge1', '72.gf1', '72.gg1', '96.bh1', '96.bt1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [37882213052, 604926858, 526, 647, 1862886, 2588323], 'label': '3456.oc.24.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '24.dz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.dz1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935857
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1728.47874', 'aut_weyl_index': 24, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.b1', '12.n1', '12.p1', '12.bk1', '12.bl1', '12.ca1', '12.cd1', '18.e1', '18.l1'], 'core': '12.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085385, 38480884412, 526, 647, 1862886, 1968991665, 2588323, 604203618], 'label': '3456.oc.6.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935858
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.ea1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1', '12.ba1'], 'contains': ['48.dw1', '48.dz1', '48.ea1', '48.ed1', '48.eg1', '72.gh1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886, 1969352190, 13414673322, 604203366], 'label': '3456.oc.24.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.ea1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ea1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935859
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '24.eb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.158', 'aut_weyl_index': 192, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '12.ba1'], 'contains': ['48.dx1', '48.dy1', '48.eb1', '48.ed1', '48.eh1', '72.gi1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 1967536007, 38480883894, 13412085385, 1862886, 604203366], 'label': '3456.oc.24.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '24.eb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.eb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935860
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.a1', '54.b1', '54.c1', '54.d1', '54.e1', '54.f1', '54.g1', '54.h1', '54.i1', '54.j1', '54.k1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1967536007, 2951738, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201935861
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '16.c1'], 'contains': ['64.a1', '64.c1', '64.d1', '96.c1', '96.h1', '96.i1'], 'core': '192.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [602743680, 1137042, 38480520960, 2226652, 13412085120], 'label': '3456.oc.32.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '32.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935862
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '16.c1'], 'contains': ['64.a1', '64.d1', '64.e1', '96.d1', '96.k1', '96.l1', '96.m1'], 'core': '192.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [602743680, 1137042, 38480520960, 1970078819, 13412085120], 'label': '3456.oc.32.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '32.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935863
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1', '8.e1', '16.c1'], 'contains': ['64.a1', '64.b1', '96.a1', '96.n1'], 'core': '96.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1967901282, 1137042, 38480520960, 13412085120], 'label': '3456.oc.32.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '32.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935864
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 216, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '16.a1', '16.d1', '16.e1', '16.f1', '16.g1'], 'contains': ['96.b1', '96.bd1', '96.be1', '96.bg1', '96.bh1', '128.a1'], 'core': '96.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 2588323, 1863007], 'label': '3456.oc.32.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '96.226'}
-
id: 201935865
{'ambient': '3456.oc', 'aut_centralizer_order': 27, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 216, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '16.b1', '16.h1'], 'contains': ['96.bp1', '96.bq1', '96.br1', '96.bs1', '96.bt1', '128.a1'], 'core': '384.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [1137421, 2587950, 38480883894, 1862886, 604203366], 'label': '3456.oc.32.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '32.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
-
id: 201935866
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1', '16.c1'], 'contains': ['64.b1', '64.c1', '64.e1', '96.cb1', '96.cc1', '96.ce1'], 'core': '192.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1967901282, 1137042, 38480520960, 2226652], 'label': '3456.oc.32.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '32.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935867
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1', '16.c1'], 'contains': ['64.b1', '64.d1', '96.cd1', '96.cg1'], 'core': '192.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1967901282, 13414311772, 1137042, 38480520960], 'label': '3456.oc.32.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '32.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935868
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.f1', '12.bu1', '18.h1', '18.o1', '24.be1', '24.bf1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967901282, 13412085385, 1862886, 647, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.6.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201935869
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '36.a1', 'complements': ['96.cb1', '96.cc1', '96.i1', '96.k1', '96.l1', '96.cd1'], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.b1', '12.r1', '18.k1', '18.l1', '18.o1'], 'contains': ['72.a1', '72.bp1', '72.bx1', '72.ds1', '72.fn1', '108.l1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [13412085385, 39799592190, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1'], 'normal_contains': ['72.a1', '144.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935870
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '36.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '96.a1', 'complements': ['96.a1', '96.g1', '96.by1', '96.bz2', '96.cf1', '96.j1', '96.cj1', '96.bv1', '96.ci1', '96.bw1', '96.ca1', '96.bz1', '96.m1', '96.bx1', '96.l1', '96.cg1', '96.ck1'], 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '12.bx1', '18.d1', '18.r1'], 'contains': ['72.b1', '108.bo1', '144.fg1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1137421, 2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': ['12.d1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '3456.oc', 'quotient_action_image': '1.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935871
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '18.m1'], 'contains': ['72.c1', '72.d1', '72.f1', '72.i1', '72.j1', '72.k1', '72.l1', '72.ck1', '72.cl1', '72.cr1', '72.ct1', '72.cy1', '72.cz1', '72.da1', '72.db1', '108.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 265, 13412085385, 38481612847, 1862886, 2226652], 'label': '3456.oc.36.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935941
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1', '12.bv1', '18.h1', '18.r1', '18.s1'], 'contains': ['72.b1', '108.bn1', '144.ez1', '144.gt1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1137421, 1967901282, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935872
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.o1'], 'contains': ['72.e1', '72.f1', '72.n1', '72.o1', '72.ba1', '72.ci1', '72.cm1', '72.do1', '72.ds1', '72.dv1', '72.gi1', '108.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 2587950, 1967536007, 38480884412, 526, 1862886], 'label': '3456.oc.36.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935873
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '18.m1'], 'contains': ['72.g1', '72.h1', '72.j1', '72.l1', '72.p1', '72.s1', '72.y1', '72.cv1', '72.cx1', '72.dh1', '72.di1', '72.ef1', '72.eh1', '72.fa1', '72.ff1', '108.c1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627126, 38480884412, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.36.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935874
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '18.a1', '18.m1'], 'contains': ['72.g1', '72.i1', '72.q1', '72.x1', '72.y2', '72.cu1', '72.dg1', '72.eg1', '72.ei1', '72.fc1', '72.fe1', '108.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2226652, 1863007, 13413948127], 'label': '3456.oc.36.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935875
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.k1', '18.b1', '18.m1'], 'contains': ['72.h1', '72.k1', '72.v1', '72.w1', '72.y2', '72.cw1', '72.dj1', '72.ej1', '72.ek1', '72.fg1', '72.fh1', '108.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2951738, 1863007, 13413948127], 'label': '3456.oc.36.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935876
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.l1', '18.a1', '18.b1', '18.n1'], 'contains': ['72.w1', '72.x1', '72.y2', '72.el1', '72.em1', '72.fj1', '72.fk1', '108.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2226275, 1863007, 13413948127], 'label': '3456.oc.36.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935877
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.m1', '18.a1', '18.c1', '18.m1'], 'contains': ['72.c1', '72.p1', '72.q1', '72.w1', '72.z1', '72.cf1', '72.dx1', '72.dy1', '72.dz1', '72.fq1', '72.fu1', '108.g1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 13413948127, 2951391], 'label': '3456.oc.36.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935878
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.n1', '18.b1', '18.e1', '18.m1'], 'contains': ['72.d1', '72.s1', '72.v1', '72.x1', '72.z1', '72.cg1', '72.ea1', '72.eb1', '72.ec1', '72.fv1', '72.fw1', '108.h1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38480884412, 526, 1968991665, 2588323, 13413948127], 'label': '3456.oc.36.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935879
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['12.g1', '12.i1', '12.j1', '12.k1', '12.m1', '12.n1', '12.t1', '12.v1', '12.w1', '12.x1', '12.y1', '12.z1', '12.bb1', '12.bc1', '12.bd1', '12.bn1', '12.bo1', '18.m1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 602744206, 13413948127, 2951391], 'label': '3456.oc.6.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935880
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '18.b1', '18.c1', '18.n1'], 'contains': ['72.w1', '72.z1', '72.ed1', '72.fy1', '72.fz1', '108.i1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 526, 13413948127], 'label': '3456.oc.36.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935881
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '18.a1', '18.e1', '18.n1'], 'contains': ['72.x1', '72.z1', '72.ee1', '72.ga1', '72.gb1', '108.j1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 38480884412, 526, 2588323, 13413948127], 'label': '3456.oc.36.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935882
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '18.a1', '18.b1', '18.o1'], 'contains': ['72.e1', '72.m1', '72.n1', '72.y1', '72.y2', '72.z1', '72.cj1', '72.dn1', '72.dq1', '72.eo1', '72.eo2', '72.fn1', '72.fs1', '108.k1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38480884129, 1967536007, 526, 1862886, 2588323], 'label': '3456.oc.36.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935883
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.f1', '18.c1', '18.e1', '18.o1'], 'contains': ['72.a1', '72.o1', '72.z1', '72.dr1', '72.fm1', '108.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085385, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935884
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.f1', '18.d1', '18.f1', '18.h1'], 'contains': ['72.b1', '108.l1', '144.l1', '144.r1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935885
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.r1', '18.g1'], 'contains': ['72.gf1', '108.l1', '144.m1', '144.s1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [38482336681, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1', 'old_label': '36.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935886
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.a1', '12.s1'], 'contains': ['72.r1', '72.t1', '72.bb1', '72.ep1', '72.eq1', '108.o1', '144.u1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2586614, 1967901282, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.36.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '36.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201935887
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.g1', '18.m1'], 'contains': ['72.bd1', '72.be1', '72.bg1', '72.bj1', '72.bk1', '72.bl1', '72.bm1', '72.cf1', '72.cg1', '72.cr1', '72.ct1', '72.cu1', '72.cv1', '72.cw1', '72.cx1', '108.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 265, 38481612847, 1862886, 2226652, 13414673322], 'label': '3456.oc.36.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935888
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.h1', '18.o1'], 'contains': ['72.bf1', '72.bg1', '72.bo1', '72.bp1', '72.by1', '72.ci1', '72.cj1', '72.dn1', '72.dr1', '72.dv1', '72.gi1', '108.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 1967536007, 13412085385, 38480884412, 526, 1862886], 'label': '3456.oc.36.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935942
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '12.bu1', '18.o1', '18.t1', '18.v1'], 'contains': ['72.a1', '72.dt1', '72.dv1', '72.fo1', '72.fs1', '108.bn1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967536007, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935889
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.i1', '18.m1'], 'contains': ['72.bh1', '72.bi1', '72.bk1', '72.bm1', '72.bq1', '72.bs1', '72.bw1', '72.cz1', '72.db1', '72.dg1', '72.dj1', '72.dx1', '72.ea1', '72.fa1', '72.ff1', '108.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627126, 13412085385, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.36.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935890
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['12.l1', '12.o1', '12.p1', '12.x1', '12.y1', '12.be1', '12.bp1', '12.bq1', '18.n1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 1968627499, 526, 602744206, 13413948127], 'label': '3456.oc.6.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935891
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.j1', '18.i1', '18.m1'], 'contains': ['72.bh1', '72.bj1', '72.br1', '72.bv1', '72.bw2', '72.cy1', '72.dh1', '72.dy1', '72.eb1', '72.fc1', '72.fg1', '108.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 38482338042, 2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.36.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935892
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.k1', '18.j1', '18.m1'], 'contains': ['72.bi1', '72.bl1', '72.bt1', '72.bu1', '72.bw2', '72.da1', '72.di1', '72.dz1', '72.ec1', '72.fe1', '72.fh1', '108.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 38482338042, 2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.36.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935893
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.l1', '18.i1', '18.j1', '18.n1'], 'contains': ['72.bu1', '72.bv1', '72.bw2', '72.ed1', '72.ee1', '72.fj1', '72.fk1', '108.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 38482338042, 2588202, 1967536007, 1863007, 2951391], 'label': '3456.oc.36.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935894
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.m1', '18.i1', '18.k1', '18.m1'], 'contains': ['72.bd1', '72.bq1', '72.br1', '72.bu1', '72.bx1', '72.ck1', '72.ef1', '72.eg1', '72.ej1', '72.fq1', '72.fv1', '108.g1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 39799592190, 526, 13413948127, 2951391], 'label': '3456.oc.36.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935895
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.n1', '18.j1', '18.l1', '18.m1'], 'contains': ['72.be1', '72.bs1', '72.bt1', '72.bv1', '72.bx1', '72.cl1', '72.eh1', '72.ei1', '72.ek1', '72.fu1', '72.fw1', '108.h1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 39798138294, 526, 1968991665, 2588323, 13413948127], 'label': '3456.oc.36.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935896
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.o1', '18.j1', '18.k1', '18.n1'], 'contains': ['72.bu1', '72.bx1', '72.el1', '72.fy1', '72.ga1', '108.i1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 39799592190, 526, 13413948127], 'label': '3456.oc.36.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935897
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.p1', '18.i1', '18.l1', '18.n1'], 'contains': ['72.bv1', '72.bx1', '72.em1', '72.fz1', '72.gb1', '108.j1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 39798138294, 526, 2588323, 13413948127], 'label': '3456.oc.36.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935898
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.q1', '18.i1', '18.j1', '18.o1'], 'contains': ['72.bf1', '72.bn1', '72.bo1', '72.bw1', '72.bw2', '72.bx1', '72.cm1', '72.do1', '72.dq1', '72.eo1', '72.eo2', '72.fm1', '72.fs1', '108.k1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 1967536007, 13412085385, 526, 1862886, 2588323], 'label': '3456.oc.36.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935899
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.t1', '18.m1'], 'contains': ['72.c1', '72.d1', '72.g1', '72.h1', '72.bd1', '72.be1', '72.bh1', '72.bi1', '72.bz1', '72.ca1', '72.cb1', '72.co1', '72.cq1', '72.dk1', '72.dl1', '108.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 13412085385, 38481612847, 1862886, 2226652, 1967535360], 'label': '3456.oc.36.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935900
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.u1', '18.o1'], 'contains': ['72.e1', '72.m1', '72.o1', '72.ba1', '72.bf1', '72.bn1', '72.bp1', '72.by1', '72.bz1', '72.cc1', '72.ce1', '72.ch1', '72.dm1', '72.dt1', '72.gh1', '108.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 2587950, 38480884412, 526, 1862886, 1967535360], 'label': '3456.oc.36.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935901
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['12.bc1', '12.be1', '12.bf1', '12.bh1', '12.bi1', '12.bl1', '12.bm1', '12.bn1', '12.bq1', '18.p1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 13412085385, 1968627499, 526, 602744206, 2951391], 'label': '3456.oc.6.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935902
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.s1', '12.v1', '18.m1'], 'contains': ['72.i1', '72.k1', '72.p1', '72.s1', '72.bj1', '72.bl1', '72.bq1', '72.bs1', '72.ca1', '72.cb1', '72.cd1', '72.dd1', '72.de1', '72.er1', '72.ev1', '108.o1'], 'core': '144.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 2226652, 2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.36.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935903
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.w1', '18.m1'], 'contains': ['72.j1', '72.q1', '72.v1', '72.bk1', '72.br1', '72.bt1', '72.ca1', '72.cd2', '72.dc1', '72.et1', '72.ew1', '108.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38482338042, 2588202, 2226652, 1863007, 13413948127, 1967535360], 'label': '3456.oc.36.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935904
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.x1', '18.m1', '18.n1'], 'contains': ['72.l1', '72.w1', '72.x1', '72.bm1', '72.bu1', '72.bv1', '72.cb1', '72.cd2', '72.df1', '72.ex1', '72.ey1', '108.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1863007, 13413948127, 2951391, 1967535360], 'label': '3456.oc.36.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201935943
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '12.bv1', '18.u1'], 'contains': ['72.du1', '72.dw1', '72.fp1', '72.ft1', '72.ge1', '108.bn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 1967536007, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '36.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935905
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.y1', '18.m1', '18.n1', '18.o1'], 'contains': ['72.f1', '72.n1', '72.y1', '72.y2', '72.z1', '72.bg1', '72.bo1', '72.bw1', '72.bw2', '72.bx1', '72.bz1', '72.cc1', '72.cd1', '72.cd2', '72.cn1', '72.dp1', '72.en1', '72.en2', '72.fo1', '108.r1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38480884129, 526, 1862886, 2588323, 1967535360], 'label': '3456.oc.36.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935906
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.z1', '18.m1'], 'contains': ['72.cf1', '72.cg1', '72.ck1', '72.cl1', '72.cn1', '72.co1', '72.cq1', '72.dc1', '72.dd1', '72.de1', '72.df1', '72.dg1', '72.dh1', '72.di1', '72.dj1', '108.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 38481612847, 1862886, 2226652, 13414673322, 1967535360], 'label': '3456.oc.36.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935907
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.ba1', '18.o1'], 'contains': ['72.ch1', '72.cj1', '72.cm1', '72.cn1', '72.dp1', '72.dq1', '72.dr1', '72.ds1', '72.dt1', '72.gh1', '72.gi1', '108.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 13412085385, 38480884412, 526, 1862886, 1967535360], 'label': '3456.oc.36.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '36.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201935908
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bb1', '18.m1'], 'contains': ['72.cu1', '72.cw1', '72.cy1', '72.da1', '72.dc1', '72.df1', '72.dk1', '72.dl1', '72.dx1', '72.ea1', '72.ef1', '72.eh1', '72.en1', '72.er1', '72.ev1', '108.u1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 38480884412, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.36.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '36.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935909
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bc1', '18.m1', '18.p1'], 'contains': ['72.cv1', '72.cz1', '72.dd1', '72.dk1', '72.dy1', '72.ec1', '72.eg1', '72.ek1', '72.en2', '72.et1', '72.ey1', '108.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38482338042, 2588202, 2226652, 1863007, 1967535360], 'label': '3456.oc.36.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935910
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bd1', '18.m1', '18.q1'], 'contains': ['72.cx1', '72.db1', '72.de1', '72.dl1', '72.dz1', '72.eb1', '72.ei1', '72.ej1', '72.en2', '72.ew1', '72.ex1', '108.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38482338042, 2588202, 1863007, 2951391, 1967535360], 'label': '3456.oc.36.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935911
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.be1', '18.n1', '18.p1', '18.q1'], 'contains': ['72.ed1', '72.ee1', '72.el1', '72.em1', '72.en2', '72.ex1', '72.ey1', '108.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 38482338042, 2588202, 2951738, 1863007, 1967535360], 'label': '3456.oc.36.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935912
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['12.bd1', '12.be1', '12.bg1', '12.bj1', '12.bk1', '12.bm1', '12.bo1', '12.bp1', '18.q1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 13412085385, 1968627499, 526, 602744206], 'label': '3456.oc.6.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935913
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bf1', '18.a1', '18.i1', '18.p1'], 'contains': ['72.dy1', '72.ee1', '72.eg1', '72.em1', '72.eo1', '72.fc1', '72.fk1', '108.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 13412085385, 2226652, 1863007], 'label': '3456.oc.36.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935914
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bg1', '18.a1', '18.j1', '18.q1'], 'contains': ['72.dz1', '72.ee1', '72.ei1', '72.el1', '72.eo1', '72.fe1', '72.fj1', '108.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 13412085385, 2226275, 1863007], 'label': '3456.oc.36.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935915
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bg1', '18.b1', '18.i1', '18.q1'], 'contains': ['72.eb1', '72.ed1', '72.ej1', '72.em1', '72.eo1', '72.fg1', '72.fj1', '108.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 13412085385, 1863007, 2951391], 'label': '3456.oc.36.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935916
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.bh1', '18.b1', '18.j1', '18.p1'], 'contains': ['72.ec1', '72.ed1', '72.ek1', '72.el1', '72.eo1', '72.fh1', '72.fk1', '108.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2951738, 13412085385, 1863007], 'label': '3456.oc.36.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935917
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bi1', '18.c1', '18.i1', '18.p1'], 'contains': ['72.dy1', '72.ed1', '72.fm1', '72.fq1', '72.fz1', '108.bb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 13412085385, 526, 2951391], 'label': '3456.oc.36.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935918
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bj1', '18.c1', '18.j1', '18.q1'], 'contains': ['72.dz1', '72.ed1', '72.fm1', '72.fu1', '72.fy1', '108.bc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 13412085385, 526], 'label': '3456.oc.36.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935919
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bk1', '18.e1', '18.i1', '18.q1'], 'contains': ['72.eb1', '72.ee1', '72.fm1', '72.fv1', '72.gb1', '108.bd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 38480884412, 526, 2588323], 'label': '3456.oc.36.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935920
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bl1', '18.e1', '18.j1', '18.p1'], 'contains': ['72.ec1', '72.ee1', '72.fm1', '72.fw1', '72.ga1', '108.be1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 13412085385, 38480884412, 526, 1968991665, 2588323], 'label': '3456.oc.36.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935921
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bi1', '18.a1', '18.k1', '18.p1'], 'contains': ['72.eg1', '72.el1', '72.fn1', '72.fq1', '72.ga1', '108.bb1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 13412085385, 39799592190, 526, 2951391], 'label': '3456.oc.36.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935922
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bk1', '18.a1', '18.l1', '18.q1'], 'contains': ['72.ei1', '72.em1', '72.fn1', '72.fu1', '72.gb1', '108.bd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 39798138294, 13412085385, 526, 2588323], 'label': '3456.oc.36.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935923
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20736.nl', 'aut_weyl_index': 2, 'centralizer': '3456.a1', 'complements': ['1728.e1', '1728.h1', '1728.j1', '1728.a1', '1728.d1', '1728.g1', '1728.f1', '1728.i1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '6.d1', '6.h1', '6.i1', '6.j1', '8.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 13412085385, 38480884412, 526, 647, 1862886, 1968991665, 2588323, 604203618], 'label': '3456.oc.2.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
-
id: 201935924
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.d1', '12.bu1', '12.cb1', '18.r1', '18.t1', '24.cz1'], 'core': '12.d1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967901282, 1862886, 2951738, 647, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.6.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201935925
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bj1', '18.b1', '18.k1', '18.q1'], 'contains': ['72.ej1', '72.el1', '72.fn1', '72.fv1', '72.fy1', '108.bc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 13412085385, 39799592190, 526], 'label': '3456.oc.36.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201935926
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bl1', '18.b1', '18.l1', '18.p1'], 'contains': ['72.ek1', '72.em1', '72.fn1', '72.fw1', '72.fz1', '108.be1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 39798138294, 13412085385, 526, 1968991665, 2588323], 'label': '3456.oc.36.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935927
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bm1', '18.o1', '18.p1', '18.q1'], 'contains': ['72.ch1', '72.ci1', '72.dm1', '72.dn1', '72.do1', '72.dp1', '72.en1', '72.en2', '72.eo1', '72.eo2', '72.fm1', '72.fn1', '72.fo1', '108.bf1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 13412085385, 526, 1862886, 2588323, 1967535360], 'label': '3456.oc.36.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935928
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bn1', '18.m1', '18.p1', '18.t1'], 'contains': ['72.co1', '72.cr1', '72.er1', '72.et1', '72.ex1', '72.fa1', '72.fc1', '72.fh1', '72.fo1', '72.fq1', '72.fw1', '108.bg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 2951391], 'label': '3456.oc.36.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935929
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.bn1', '18.u1'], 'contains': ['72.cp1', '72.cs1', '72.es1', '72.eu1', '72.ez1', '72.fb1', '72.fd1', '72.fi1', '72.fp1', '72.fr1', '72.fx1', '108.bg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 1968627499, 526, 37883666682, 2951391], 'label': '3456.oc.36.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '36.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935930
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bo1', '18.m1', '18.q1', '18.v1'], 'contains': ['72.cq1', '72.ct1', '72.ev1', '72.ew1', '72.ey1', '72.fe1', '72.ff1', '72.fg1', '72.fo1', '72.fu1', '72.fv1', '108.bh1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 13415398178], 'label': '3456.oc.36.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935931
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bp1', '18.n1', '18.q1', '18.t1'], 'contains': ['72.ex1', '72.fj1', '72.fo1', '72.fy1', '72.gb1', '108.bi1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 1968627499, 526], 'label': '3456.oc.36.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935932
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bq1', '18.n1', '18.p1', '18.v1'], 'contains': ['72.ey1', '72.fk1', '72.fo1', '72.fz1', '72.ga1', '108.bj1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 13415397945], 'label': '3456.oc.36.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935933
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.bp1', '18.u1'], 'contains': ['72.ez1', '72.fl1', '72.fp1', '72.gc1', '72.gd1', '108.bi1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 1968627499, 526, 37883666682], 'label': '3456.oc.36.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '36.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935934
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.br1', '18.a1', '18.i1', '18.t1'], 'contains': ['72.fc1', '72.fj1', '72.fq1', '72.fs1', '72.gb1', '108.bk1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 2951391], 'label': '3456.oc.36.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935935
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1'], 'contains': ['12.bv1', '12.bx1', '12.ce1', '18.r1', '18.u1', '24.da1'], 'core': '36.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 1137421, 2951738, 1967901282, 526, 647, 1862886, 2588323], 'label': '3456.oc.6.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '6.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201935936
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.br1', '18.u1'], 'contains': ['72.fd1', '72.fl1', '72.fr1', '72.ft1', '72.gd1', '108.bk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 526, 37883666682, 2951391], 'label': '3456.oc.36.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '36.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935937
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bs1', '18.a1', '18.j1', '18.v1'], 'contains': ['72.fe1', '72.fk1', '72.fs1', '72.fu1', '72.ga1', '108.bl1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 13415398178], 'label': '3456.oc.36.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935938
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bs1', '18.b1', '18.i1', '18.v1'], 'contains': ['72.fg1', '72.fk1', '72.fs1', '72.fv1', '72.fz1', '108.bl1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 13415397945], 'label': '3456.oc.36.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935939
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bt1', '18.b1', '18.j1', '18.t1'], 'contains': ['72.fh1', '72.fj1', '72.fs1', '72.fw1', '72.fy1', '108.bm1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 2951738, 526], 'label': '3456.oc.36.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935940
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.bt1', '18.u1'], 'contains': ['72.fi1', '72.fl1', '72.ft1', '72.fx1', '72.gc1', '108.bm1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 2951738, 526, 37883666682], 'label': '3456.oc.36.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '36.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935944
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '12.bw1', '18.c1', '18.k1', '18.t1'], 'contains': ['72.a1', '72.fq1', '72.fy1', '108.bo1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2951738, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935945
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1', '12.bx1', '18.u1'], 'contains': ['72.fr1', '72.gc1', '72.ge1', '108.bo1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.36.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '36.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935946
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.e1', '3.a1'], 'contains': ['12.e1', '12.bu1', '12.by1', '18.s1', '18.v1', '24.db1'], 'core': '12.e1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967901282, 1862886, 647, 13415398178, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.6.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201935947
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.by1', '12.bz1', '12.ca1', '18.c1', '18.l1', '18.v1'], 'contains': ['72.a1', '72.fu1', '72.fz1', '108.bp1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 647, 13415398178, 38480884412, 2588323, 526], 'label': '3456.oc.36.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935948
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.ca1', '18.e1', '18.k1', '18.v1'], 'contains': ['72.a1', '72.fv1', '72.ga1', '108.bp1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39799592190, 526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.36.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935949
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.by1', '18.d1', '18.f1', '18.s1'], 'contains': ['72.b1', '108.bp1', '144.fm1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.36.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935950
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.e1', '12.bz1', '18.g1'], 'contains': ['72.gf1', '108.bp1', '144.fn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [39798141540, 526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.36.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '36.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935951
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cb1', '12.cc1', '12.cd1', '18.e1', '18.l1', '18.t1'], 'contains': ['72.a1', '72.fw1', '72.gb1', '108.bq1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884412, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.36.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935952
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1', '12.ce1', '12.cf1', '18.u1'], 'contains': ['72.fx1', '72.gd1', '72.ge1', '108.bq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37882213052, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.36.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '36.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935953
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1', '12.ce1', '18.f1', '18.r1'], 'contains': ['72.b1', '108.bq1', '144.fr1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1137421, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.36.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935954
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.cb1', '12.cc1', '12.cf1', '18.g1'], 'contains': ['72.gf1', '108.bq1', '144.fs1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38482336681, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.36.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1', 'old_label': '36.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935955
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cc1', '12.ce1', '12.cf1'], 'contains': ['72.gg1', '108.bq1', '144.ft1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37883665321, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.36.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.da1', 'old_label': '36.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201935956
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '72.a1', 'complements': ['72.ep1', '72.r1', '72.t1', '72.u1', '72.eq1'], 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '24.a1', '24.s1', '24.x1', '24.bb1', '24.bc1'], 'contains': ['96.b1', '96.e1', '96.q1', '144.a1', '144.k1'], 'core': '48.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [604203487, 38480884412, 2588323, 1863007, 13413948127], 'label': '3456.oc.48.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': ['12.b1', '24.a1'], 'normal_contains': ['96.b1', '144.a1', '192.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935957
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3456.hx', 'aut_weyl_index': 12, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.b1'], 'contains': ['12.c1', '12.bn1', '12.bp1', '12.br1', '12.bt1', '12.bw1', '12.cd1', '18.t1', '18.u1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1967536007, 2951738, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.6.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935958
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': ['72.r1', '72.t1', '72.u1'], 'conjugacy_class_count': 3, 'contained_in': ['16.d1', '24.a1', '24.cx1', '24.dc1', '24.de1', '24.dp1'], 'contains': ['96.b1', '96.r1', '96.v1', '144.fa1', '144.fb1'], 'core': '48.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38480884412, 2588323, 1863007, 1967535360], 'label': '3456.oc.48.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': ['12.c1', '24.a1'], 'normal_contains': ['96.b1', '192.b1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
-
id: 201935959
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.f1', '16.a1', '24.d1', '24.e1', '24.be1'], 'contains': ['96.bd1', '144.k1', '144.l1', '144.m1', '192.c1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 38480884412, 2588323, 1863007, 13413948127], 'label': '3456.oc.48.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '48.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201935960
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '16.b1', '24.bf1'], 'contains': ['96.bp1', '144.q1', '144.r1', '144.s1', '192.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1137421, 2587950, 38480883894, 13414673070, 1862886], 'label': '3456.oc.48.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bf1', 'old_label': '48.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
-
id: 201935961
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.g1', '24.h1', '24.i1', '24.r1', '24.bc1', '24.bg1'], 'contains': ['96.e1', '96.f1', '96.o1', '96.t1', '96.bi1', '144.b1', '144.v1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.48.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935962
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.j1', '24.l1', '24.m1', '24.s1', '24.t1', '24.bh1'], 'contains': ['96.e1', '96.h1', '96.s1', '96.w1', '96.bu1', '144.c1', '144.w1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 38480884533, 13412085120], 'label': '3456.oc.48.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935963
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.k1', '24.p1', '24.bb1', '24.bb2', '24.bg1'], 'contains': ['96.e1', '96.j1', '96.t1', '96.x1', '96.bw1', '144.d1', '144.x1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1967536007, 1134693, 38480884533], 'label': '3456.oc.48.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935964
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.k1', '24.m1', '24.n1', '24.x1', '24.y1', '24.bh1'], 'contains': ['96.e1', '96.m1', '96.w1', '96.y1', '96.bx1', '144.e1', '144.y1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 13413948379, 1970078819, 38481613099], 'label': '3456.oc.48.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935965
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.k1', '24.n1', '24.o1', '24.s1', '24.z1', '24.bi1'], 'contains': ['96.e1', '96.z1', '96.ba1', '144.f1', '144.z1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 38480884533, 13412085120], 'label': '3456.oc.48.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201935966
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.j1', '24.l1', '24.o1', '24.x1', '24.ba1', '24.bi1'], 'contains': ['96.e1', '96.ba1', '96.bb1', '144.g1', '144.ba1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 1970078440, 13413948379, 38481613099], 'label': '3456.oc.48.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935967
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.h1', '24.p1', '24.q1', '24.bb1', '24.bb2', '24.bj1'], 'contains': ['96.e1', '96.g1', '96.j1', '96.p1', '96.u1', '96.bv1', '96.ca1', '144.h1', '144.bb1'], 'core': '192.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 1134693, 1968627499, 38480884533, 13412085120], 'label': '3456.oc.48.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935968
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3456.hx', 'aut_weyl_index': 12, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '3.b1'], 'contains': ['12.c1', '12.bo1', '12.bq1', '12.bs1', '12.ca1', '18.v1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1862886, 647, 13415398178, 1967536007, 2588323, 526, 38480884412, 604203618], 'label': '3456.oc.6.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201935969
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.a1', '24.i1', '24.l1', '24.n1', '24.q1', '24.bb2'], 'contains': ['96.e1', '96.g1', '96.q1', '96.v1', '96.bz1', '144.i1', '144.bc1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 1968627378, 38480884533], 'label': '3456.oc.48.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935970
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.l2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '24.m1', '24.o1', '24.q1', '24.bb1', '24.bk1'], 'contains': ['96.e1', '96.g1', '96.q2', '96.v2', '96.bz2', '144.i2', '144.bc2'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 13413948127, 38480884533], 'label': '3456.oc.48.l2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.l2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935971
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '24.q1', '24.r1', '24.bc1', '24.bj1'], 'contains': ['96.e1', '96.f1', '96.p1', '96.bc1', '96.bj1', '144.j1', '144.bd1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1862886, 2588323, 38480884533, 13412085120, 604203366], 'label': '3456.oc.48.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201935972
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.a1', '16.a1', '24.u1', '24.v1', '24.be1'], 'contains': ['96.bd1', '144.a1', '144.l1', '192.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39799592563, 1137421, 2588323, 1863007, 13413948127], 'label': '3456.oc.48.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '48.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935973
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.r1', '16.a1', '24.w1'], 'contains': ['96.be1', '144.a1', '144.m1', '192.e1'], 'core': '144.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [39799592563, 604926858, 2588323, 1863007, 13413948127], 'label': '3456.oc.48.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '48.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201935974
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '36.cq1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.y1', '24.z1', '24.ba1', '24.bb2', '24.bc1', '24.bk1'], 'contains': ['96.e1', '96.q2', '96.bf1', '144.k2', '144.be1'], 'core': '192.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38480884129, 13413948258, 1863138, 2588323, 604203618], 'label': '3456.oc.48.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935975
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.p1', '24.q1', '24.bd1', '24.bg1'], 'contains': ['96.f1', '96.g1', '96.j1', '96.bi1', '96.bm1', '96.bw1', '96.ci1', '144.n1', '144.bf1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1967536007, 38481612726, 1862886, 604203366], 'label': '3456.oc.48.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935976
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.i1', '24.q1', '24.bd1', '24.bj1'], 'contains': ['96.f1', '96.g1', '96.bj1', '96.bn1', '96.bv1', '144.o1', '144.bg1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352442, 13414673322, 604203366], 'label': '3456.oc.48.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935977
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.h1', '24.p1', '24.bl1'], 'contains': ['96.f1', '96.j1', '96.bl1', '96.bo1', '96.cj1', '144.p1', '144.bh1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352190, 13412085120, 604203366], 'label': '3456.oc.48.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935978
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '16.b1', '24.bf1'], 'contains': ['96.bp1', '144.r1', '144.bi1', '192.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1137421, 2587950, 39799592190, 13414673070, 1862886], 'label': '3456.oc.48.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '48.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
-
id: 201935979
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '4608.dp', 'aut_weyl_index': 9, 'centralizer': '384.a1', 'complements': ['432.dm1', '432.o1', '432.dn1', '432.r1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['24.b1', '24.c1', '24.dx1', '24.dy1', '24.dz1', '32.d1', '32.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1137421, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '3456.oc', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '384.20163'}
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id: 201935980
{'ambient': '3456.oc', 'aut_centralizer_order': 9, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.r1', '16.b1'], 'contains': ['96.bq1', '144.s1', '144.bi1', '192.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [2587950, 604926858, 39799592190, 13414673070, 1862886], 'label': '3456.oc.48.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '48.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
-
id: 201935981
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '24.r1', '24.bd1', '24.bl1'], 'contains': ['96.f1', '96.bl1', '96.br1', '144.q1', '144.bi1'], 'core': '192.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1862886, 604203366], 'label': '3456.oc.48.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
-
id: 201935982
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.bh1'], 'contains': ['96.g1', '96.h1', '96.m1', '96.bu1', '96.bx1', '96.ch1', '96.ck1', '144.t1', '144.bj1'], 'core': '192.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 1968627247, 38480520960, 2226652, 13413948127], 'label': '3456.oc.48.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '48.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935983
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.s1', '16.c1'], 'contains': ['96.c1', '96.d1', '96.i1', '96.k1', '96.n1', '96.cb1', '96.cd1', '144.u1', '144.bm1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1967901282, 1137042, 38480520960, 2226652, 13412085120], 'label': '3456.oc.48.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '48.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935984
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '24.bg1', '24.bh1', '24.bi1', '24.bj1', '24.bk1'], 'contains': ['96.a1', '96.e1', '96.g1', '96.r1', '96.by1', '144.bk1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1134693, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.48.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935985
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1', '24.bj1', '24.bl1'], 'contains': ['96.a1', '96.f1', '96.j1', '96.bk1', '96.cf1', '144.bl1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38481612726, 1862886, 1967535360, 13412085120, 604203366], 'label': '3456.oc.48.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201935986
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '24.bh1'], 'contains': ['96.a1', '96.h1', '96.m1', '96.ce1', '96.cg1', '144.bm1'], 'core': '96.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652, 1967535360, 13412085120], 'label': '3456.oc.48.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '48.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935987
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.r1', '24.bm1', '24.bo1', '24.bq1', '24.cm1', '24.do1'], 'contains': ['96.o1', '96.p1', '96.bi1', '96.bj1', '96.bl1', '144.bn1', '144.bp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085385, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.48.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201935988
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '24.bc1', '24.bn1', '24.bp1', '24.bq1', '24.br1', '24.cm1'], 'contains': ['96.o1', '96.q1', '96.q2', '96.bj1', '144.bo1', '144.bq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [526, 1862886, 13414673191, 38481612978, 604203618], 'label': '3456.oc.48.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935989
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bg1', '24.bm1', '24.br1', '24.bs1', '24.bt1', '24.cn1', '24.dp1'], 'contains': ['96.o1', '96.r1', '96.x1', '96.bk1', '96.bm1', '144.br1', '144.bs1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [526, 1862886, 38481612978, 604203618, 1967535360], 'label': '3456.oc.48.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201935990
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '4.f1'], 'contains': ['16.a1', '16.e1', '16.f1', '24.d1', '24.s1', '24.u1', '32.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.8.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '288.1028'}
-
id: 201935991
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.f1', '24.bn1', '24.bs1', '24.bu1', '24.dq1'], 'contains': ['96.o1', '96.s1', '96.z1', '144.bt1', '144.bu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 1862886, 2226652], 'label': '3456.oc.48.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201935992
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.h1', '24.bq1', '24.cn1', '24.co1', '24.dr1'], 'contains': ['96.o1', '96.u1', '96.bm1', '96.bn1', '96.bo1', '144.bv1', '144.bw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.48.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935993
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.i1', '24.bo1', '24.bu1', '24.bv1', '24.co1', '24.dp1'], 'contains': ['96.o1', '96.v1', '96.v2', '96.bn1', '144.bx1', '144.by1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1969352563, 526, 1862886, 38481612978, 604203618], 'label': '3456.oc.48.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201935994
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.g1', '24.bn1', '24.bp1', '24.bt1', '24.bv1', '24.ds1'], 'contains': ['96.o1', '96.w1', '96.ba1', '144.bz1', '144.ca1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 13413586612, 1862886], 'label': '3456.oc.48.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201935995
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.g1', '24.bp1', '24.bs1', '24.bu1', '24.dt1'], 'contains': ['96.o1', '96.y1', '96.bb1', '144.cb1', '144.cc1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884412, 526, 1968991665, 1134054, 602744206], 'label': '3456.oc.48.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201935996
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.h1', '24.p1', '24.ci1', '24.cj1', '24.cy1', '24.cy2'], 'contains': ['96.p1', '96.t1', '96.u1', '96.bv1', '96.bw1', '96.ci1', '96.cj1', '144.cd1', '144.cn1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 1134693, 1968627499, 13413948006, 38480884533], 'label': '3456.oc.48.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935997
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bj1', '24.bm1', '24.ci1', '24.ck1', '24.cx1', '24.cx2'], 'contains': ['96.p1', '96.r1', '96.bv1', '96.by1', '96.cf1', '144.co1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 602743680, 1134693, 1967535360, 38480884533], 'label': '3456.oc.48.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201935998
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.t1', '24.bn1', '24.bw1', '24.ca1', '24.ce1', '24.cp1'], 'contains': ['96.q2', '96.s1', '96.w1', '96.bu1', '144.ce1', '144.cs1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 13413948127, 38480884533], 'label': '3456.oc.48.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201935999
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.s1', '24.bn1', '24.bx1', '24.cb1', '24.ce1', '24.cq1'], 'contains': ['96.q1', '96.s1', '96.ba1', '144.cf1', '144.ct1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 2226652, 38480884533], 'label': '3456.oc.48.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936000
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '24.bb1', '24.bx1', '24.bz1', '24.cj1', '24.cx2'], 'contains': ['96.q1', '96.t1', '96.v2', '96.bv1', '144.cg1', '144.cu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1968627247, 1134693, 38480884533], 'label': '3456.oc.48.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936001
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 48, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.b1', '4.f1'], 'contains': ['16.a1', '16.f1', '16.g1', '24.e1', '24.v1', '24.w1', '24.x1', '32.b1'], 'core': '48.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [604203487, 1137421, 38480884412, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.8.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201936002
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bn2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '24.bb2', '24.bw1', '24.by1', '24.cj1', '24.cx1'], 'contains': ['96.q2', '96.t1', '96.v1', '96.bv1', '144.cg2', '144.cu2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 1968627378, 38480884533], 'label': '3456.oc.48.bn2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bn2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936003
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bn3', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.q1', '24.bo1', '24.cj1', '24.cx1', '24.cy1'], 'contains': ['96.p1', '96.v1', '96.bv1', '96.bz2', '96.ci1', '144.cp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 602743680, 1134693, 1968627378, 38480884533], 'label': '3456.oc.48.bn3', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bn3', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn3', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936004
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bn4', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.q1', '24.bo1', '24.cj1', '24.cx2', '24.cy2'], 'contains': ['96.p1', '96.v2', '96.bv1', '96.bz1', '96.ci1', '144.cp2'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 13412085385, 38480884533], 'label': '3456.oc.48.bn4', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bn4', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn4', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936005
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '24.bm1', '24.cl1', '24.cy1', '24.cy2'], 'contains': ['96.p1', '96.x1', '96.bw1', '96.ca1', '96.cj1', '144.cq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 13412085385, 38480884533], 'label': '3456.oc.48.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936006
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.y1', '24.bp1', '24.by1', '24.ca1', '24.cf1', '24.cr1'], 'contains': ['96.q2', '96.w1', '96.y1', '96.bx1', '144.ci1', '144.cv1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 1970078819, 13413219692, 38481613099], 'label': '3456.oc.48.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936007
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.n1', '24.s1', '24.bn1', '24.bz1', '24.cc1', '24.cf1', '24.cs1'], 'contains': ['96.q1', '96.w1', '96.z1', '144.ch1', '144.cx1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 2951738, 38480884533], 'label': '3456.oc.48.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936008
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.x1', '24.bp1', '24.bz1', '24.cc1', '24.ce1', '24.ct1'], 'contains': ['96.q1', '96.w1', '96.bb1', '144.cj1', '144.cw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 1970078440, 13414673322, 38481613099], 'label': '3456.oc.48.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936009
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.n1', '24.x1', '24.bp1', '24.bx1', '24.cb1', '24.cf1', '24.cu1'], 'contains': ['96.q1', '96.y1', '96.ba1', '144.ck1', '144.cy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 1970078819, 13414673322, 38481613099], 'label': '3456.oc.48.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936010
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.o1', '24.z1', '24.bn1', '24.by1', '24.cd1', '24.cf1', '24.cp1'], 'contains': ['96.q2', '96.z1', '96.ba1', '144.cl1', '144.cz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 13413948127, 38480884533], 'label': '3456.oc.48.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936011
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.o1', '24.ba1', '24.bp1', '24.bw1', '24.cd1', '24.ce1', '24.cr1'], 'contains': ['96.q2', '96.ba1', '96.bb1', '144.cm1', '144.da1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1863259, 602743680, 1970078440, 13413219692, 38481613099], 'label': '3456.oc.48.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936012
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.c1', '4.f1'], 'contains': ['16.a1', '16.d1', '24.a1', '24.be1', '32.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1967901282, 1863007, 2586614, 604203487, 13413948127, 2588323, 38480884412], 'label': '3456.oc.8.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201936013
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '24.bb1', '24.bq1', '24.cj1', '24.ck1', '24.cl1', '24.cy1'], 'contains': ['96.p1', '96.q1', '96.u1', '96.bv1', '96.bw1', '96.bz2', '96.ca1', '144.cr1', '144.db1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 1968627499, 38480884533], 'label': '3456.oc.48.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936014
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bv2', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '24.bb2', '24.bq1', '24.cj1', '24.ck1', '24.cl1', '24.cy2'], 'contains': ['96.p1', '96.q2', '96.u1', '96.bv1', '96.bw1', '96.bz1', '96.ca1', '144.cr2', '144.db2'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13412085646, 602743680, 1134693, 1968627499, 38480884533], 'label': '3456.oc.48.bv2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.bv2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936015
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '24.br1', '24.cb1', '24.cc1', '24.ck1', '24.cx2'], 'contains': ['96.q1', '96.r1', '96.by1', '96.bz1', '144.dc1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 1967535360, 38480884533], 'label': '3456.oc.48.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936016
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.bw2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bk1', '24.br1', '24.ca1', '24.cd1', '24.ck1', '24.cx1'], 'contains': ['96.q2', '96.r1', '96.by1', '96.bz2', '144.dc2'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1134693, 13413948127, 1967535360, 38480884533], 'label': '3456.oc.48.bw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bw2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936017
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb1', '24.bb2', '24.br1', '24.ce1', '24.cf1', '24.cl1'], 'contains': ['96.q1', '96.q2', '96.x1', '96.ca1', '144.dd1', '144.dd2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 13413948127, 38480884533], 'label': '3456.oc.48.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936018
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bh1', '24.bs1', '24.ca1', '24.cb1', '24.cg1', '24.dc1', '24.dd1'], 'contains': ['96.r1', '96.s1', '96.y1', '96.ce1', '96.ch1', '144.de1', '144.df1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.48.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936019
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bg1', '24.cg1', '24.ch1', '24.ci1', '24.cx1', '24.cx2'], 'contains': ['96.r1', '96.t1', '96.cf1', '96.ci1', '144.dg1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 1967535360, 38480884533], 'label': '3456.oc.48.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936020
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bh1', '24.bt1', '24.ca1', '24.cc1', '24.ch1', '24.de1', '24.df1'], 'contains': ['96.r1', '96.w1', '96.cg1', '96.ck1', '144.dh1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 13414311772, 1967535360, 38480884533], 'label': '3456.oc.48.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936021
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bi1', '24.bs1', '24.cc1', '24.cd1', '24.ch1', '24.dc1', '24.dg1'], 'contains': ['96.r1', '96.z1', '96.bb1', '144.di1', '144.dk1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.48.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936022
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bi1', '24.bt1', '24.cb1', '24.cd1', '24.cg1', '24.de1', '24.dh1'], 'contains': ['96.r1', '96.ba1', '144.dj1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 13415036858, 1134693, 1967535360, 38480884533], 'label': '3456.oc.48.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936023
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['16.b1', '16.h1', '24.bf1', '24.bl1', '32.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 8, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1967901282, 1862886, 1137042, 604203366], 'label': '3456.oc.8.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '8.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '432.749'}
-
id: 201936024
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.j1', '24.bw1', '24.bx1', '24.cg1', '24.cp1', '24.cq1'], 'contains': ['96.s1', '96.t1', '96.ba1', '144.dl1', '144.dm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 2226652, 38480884533], 'label': '3456.oc.48.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936025
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.m1', '24.bu1', '24.bx1', '24.dd1', '24.di1'], 'contains': ['96.s1', '96.v2', '96.y1', '96.ch1', '144.dn1', '144.do1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 2226652, 38480884533], 'label': '3456.oc.48.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936026
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.l1', '24.bu1', '24.bw1', '24.dc1', '24.dj1'], 'contains': ['96.s1', '96.v1', '96.bb1', '144.dp1', '144.dq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 1968627378, 38480884533], 'label': '3456.oc.48.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936027
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.j1', '24.bs1', '24.ce1', '24.di1', '24.dj1'], 'contains': ['96.s1', '96.x1', '96.bb1', '144.dr1', '144.ds1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 2226652, 38480884533], 'label': '3456.oc.48.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936028
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '24.k1', '24.by1', '24.bz1', '24.ch1', '24.cp1', '24.cs1'], 'contains': ['96.t1', '96.w1', '96.z1', '144.dt1', '144.dx1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 2951738, 38480884533], 'label': '3456.oc.48.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936029
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.j1', '24.bw1', '24.bz1', '24.ch1', '24.cr1', '24.ct1'], 'contains': ['96.t1', '96.w1', '96.bb1', '144.du1', '144.dw1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1863259, 602743680, 1970078440, 38481613099], 'label': '3456.oc.48.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936030
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '24.k1', '24.bx1', '24.by1', '24.cg1', '24.cr1', '24.cu1'], 'contains': ['96.t1', '96.y1', '96.ba1', '144.dv1', '144.dy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1863259, 602743680, 1970078819, 38481613099], 'label': '3456.oc.48.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936031
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '24.n1', '24.bv1', '24.bw1', '24.by1', '24.de1', '24.dk2'], 'contains': ['96.v1', '96.w1', '96.ba1', '144.dz1', '144.ea1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 13415036858, 1134693, 1968627378, 38480884533], 'label': '3456.oc.48.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936032
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.889', 'aut_weyl_index': 144, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.m1', '24.bv1', '24.bz1', '24.df1', '24.dk1'], 'contains': ['96.v2', '96.w1', '96.ck1', '144.eb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 13414311772, 38480884533], 'label': '3456.oc.48.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936033
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.n1', '24.bu1', '24.by1', '24.dc1', '24.dl1'], 'contains': ['96.v1', '96.y1', '96.z1', '144.ec1', '144.ed1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 1968627378, 38480884533], 'label': '3456.oc.48.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936034
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '41472.kr', 'aut_weyl_index': 1, 'centralizer': '3456.a1', 'complements': ['1728.f1', '1728.k1', '1728.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.b1', '6.k1', '8.d1', '8.e1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [526, 647, 38480884412, 2588323, 1137421, 13412085385, 1862886, 1967901282, 604203618], 'label': '3456.oc.2.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
-
id: 201936035
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.d1', '4.f1'], 'contains': ['16.d1', '16.e1', '16.g1', '24.cz1', '24.da1', '24.dc1', '32.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1967901282, 1863007, 2226652, 2586614, 604203487, 2588323, 38480884412], 'label': '3456.oc.8.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201936036
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.o1', '24.bu1', '24.bz1', '24.dg1', '24.di1'], 'contains': ['96.v2', '96.z1', '96.bb1', '144.ee1', '144.eg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 2951738, 38480884533], 'label': '3456.oc.48.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936037
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.889', 'aut_weyl_index': 144, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.o1', '24.bv1', '24.bx1', '24.dh1', '24.dk1'], 'contains': ['96.v2', '96.ba1', '144.ef1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627247, 13415036858, 1134693, 38480884533], 'label': '3456.oc.48.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936038
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '24.k1', '24.bt1', '24.ce1', '24.cf1', '24.dk1', '24.dk2'], 'contains': ['96.w1', '96.x1', '96.ba1', '144.eh1', '144.ei1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 13415036858, 1967536007, 1134693, 38480884533], 'label': '3456.oc.48.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936039
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.cq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.k1', '24.bs1', '24.cf1', '24.di1', '24.dl1'], 'contains': ['96.x1', '96.y1', '96.z1', '144.ej1', '144.ek1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 2951738, 38480884533], 'label': '3456.oc.48.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936040
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.cr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '24.r1', '24.ci1', '24.cj1', '24.do1'], 'contains': ['96.p1', '96.t1', '96.bc1', '96.bi1', '96.bl1', '144.el1', '144.en1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.48.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cr1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936041
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.cs1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '24.bc1', '24.cj1', '24.ck1', '24.cl1', '24.cm1', '24.do1'], 'contains': ['96.p1', '96.q1', '96.q2', '96.bc1', '96.bi1', '96.bj1', '144.em1', '144.eo1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13412085385, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.48.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936042
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.ct1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bj1', '24.ci1', '24.ck1', '24.cn1', '24.dp1'], 'contains': ['96.r1', '96.u1', '96.bc1', '96.bk1', '96.bn1', '144.ep1', '144.eq1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 2588323, 1967535360, 38480884533, 604203366], 'label': '3456.oc.48.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ct1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936043
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.cu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.p1', '24.cl1', '24.cn1', '24.dr1'], 'contains': ['96.u1', '96.x1', '96.bc1', '96.bm1', '96.bo1', '144.er1', '144.es1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1967536007, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.48.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cu1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936044
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.cv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.q1', '24.cj1', '24.co1', '24.dp1', '24.dr1'], 'contains': ['96.u1', '96.v1', '96.v2', '96.bc1', '96.bm1', '96.bn1', '144.et1', '144.eu1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967535625, 1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.48.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936045
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '48.cw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.r1', '24.cm1', '24.cn1', '24.co1'], 'contains': ['96.o1', '96.bc1', '96.br1', '144.ev1', '144.ew1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 38480884412, 526, 1862886, 604203618], 'label': '3456.oc.48.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cw1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936046
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.e1', '4.f1'], 'contains': ['16.d1', '16.f1', '24.db1', '24.de1', '32.g1'], 'core': '48.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1863007, 13413586612, 1967901775, 604203487, 2588323, 38480884412, 2586735], 'label': '3456.oc.8.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '864.4673'}
-
id: 201936047
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb1', '24.bc1', '24.cp1', '24.cr1', '24.cx1', '24.cy2', '24.do1'], 'contains': ['96.b1', '96.p1', '96.q2', '96.t1', '144.ex1', '144.ey1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 13412085385, 38480884412, 2588323, 1863007], 'label': '3456.oc.48.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936048
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.cx2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb2', '24.bc1', '24.cq1', '24.cs1', '24.ct1', '24.cu1', '24.cv1', '24.cw1', '24.cx2', '24.cy1', '24.do1'], 'contains': ['96.p1', '96.q1', '96.t1', '96.bf1', '144.ex2', '144.ey2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 13412085385, 1863138, 2588323, 604203618], 'label': '3456.oc.48.cx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.cx2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cx2', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936049
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '48.cy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bu1', '16.d1', '24.be1', '24.cz1', '24.db1'], 'contains': ['96.bd1', '144.ez1', '144.fa1', '192.i1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967901282, 1863007, 2586614, 38480884412, 2588323], 'label': '3456.oc.48.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '48.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cy1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936050
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '48.cz1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.bv1', '16.d1', '24.da1'], 'contains': ['96.bg1', '144.ez1', '144.fb1', '192.j1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [37882213052, 2586614, 1967901282, 2588323, 1863007], 'label': '3456.oc.48.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1', 'old_label': '48.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cz1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936051
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.da1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bk1', '24.cx2', '24.dd1', '24.df1', '24.dg1', '24.dh1', '24.dp1'], 'contains': ['96.r1', '96.v2', '96.bf1', '144.fa2', '144.fb2'], 'core': '192.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [38480884129, 1863138, 2588323, 604203618, 1967535360], 'label': '3456.oc.48.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.da1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936052
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '48.db1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.e1', '24.s1', '24.cp1', '24.dc1', '24.di1', '24.dq1'], 'contains': ['96.b1', '96.s1', '96.z1', '144.fc1', '144.fd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.48.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.db1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936053
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '48.dc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 216, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1', '24.cq1', '24.dd1', '24.dj1', '24.dq1'], 'contains': ['96.s1', '96.bf1', '144.fe1', '144.ff1'], 'core': '384.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2226652, 1863007], 'label': '3456.oc.48.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936054
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '48.dd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.d1', '16.e1', '24.d1', '24.u1', '24.cz1'], 'contains': ['96.bd1', '144.fc1', '144.fg1', '192.l1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1137421, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.48.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '48.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201936055
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '48.de1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.bx1', '16.e1', '24.da1'], 'contains': ['96.bg1', '144.fd1', '144.fg1', '192.m1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [37882213052, 1137421, 2226652, 2588323, 1863007], 'label': '3456.oc.48.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '48.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.de1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201936056
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.df1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bb1', '24.cy2', '24.di1', '24.dk1', '24.dp1', '24.dr1'], 'contains': ['96.b1', '96.u1', '96.v2', '96.x1', '144.fh1', '144.fi1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 1967536007, 38480884412, 2588323, 1863007], 'label': '3456.oc.48.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936057
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.d1', '18.f1', '18.h1', '18.r1', '18.s1', '27.a1', '36.q1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967901282, 13412085385, 1862886, 2951738, 647, 526, 2588323, 1137421], 'label': '3456.oc.9.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201936058
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.df2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bb2', '24.cy1', '24.dj1', '24.dk2', '24.dl1', '24.dm1', '24.dn1', '24.dp1', '24.dr1'], 'contains': ['96.u1', '96.v1', '96.x1', '96.bf1', '144.fh2', '144.fi2'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [38480884129, 1967536007, 1863138, 2588323, 604203618], 'label': '3456.oc.48.df2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.df2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.df2', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936059
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '48.dg1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.by1', '16.f1', '24.d1', '24.v1', '24.db1'], 'contains': ['96.bd1', '144.fj1', '144.fm1', '192.p1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137300, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.48.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '48.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201936060
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '48.dh1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.bz1', '16.f1', '24.w1'], 'contains': ['96.be1', '144.fj1', '144.fn1', '192.q1'], 'core': '288.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [604926858, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.48.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '48.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dh1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201936061
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.di1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.f1', '24.s1', '24.x1', '24.cp1', '24.cr1', '24.de1', '24.dk1', '24.ds1'], 'contains': ['96.b1', '96.w1', '96.ba1', '144.fj1', '144.fl1'], 'core': '96.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.48.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.di1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936062
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.dj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '24.y1', '24.cs1', '24.ct1', '24.df1', '24.dk2', '24.ds1'], 'contains': ['96.w1', '96.bf1', '144.fk1', '144.fo1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13413586379, 604203487, 38482338042, 2588202, 1863007], 'label': '3456.oc.48.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936063
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '48.dk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.e1', '16.f1', '24.e1', '24.u1', '24.db1'], 'contains': ['96.bd1', '144.fl1', '144.fm1', '144.fn1', '192.s1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [39799592563, 1137300, 13413586612, 2588323, 1863007], 'label': '3456.oc.48.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '48.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dk1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936064
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '48.dl1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.cb1', '16.g1', '24.e1', '24.v1', '24.cz1'], 'contains': ['96.bd1', '144.fp1', '144.fr1', '144.fs1', '192.u1'], 'core': '288.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.48.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '48.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dl1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936065
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '48.dm1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.cc1', '16.g1', '24.w1'], 'contains': ['96.be1', '144.fp1', '144.fs1', '144.ft1', '192.v1'], 'core': '288.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [604926858, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.48.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '48.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dm1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936066
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.dn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.g1', '24.x1', '24.cr1', '24.dc1', '24.di1', '24.dt1'], 'contains': ['96.b1', '96.y1', '96.bb1', '144.fp1', '144.fq1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.48.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '48.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dn1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936067
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '48.do1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.ce1', '16.g1', '24.da1'], 'contains': ['96.bg1', '144.fq1', '144.fr1', '144.ft1', '192.x1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [37882213052, 1137421, 1968991665, 2588323, 1863007], 'label': '3456.oc.48.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.da1', 'old_label': '48.do1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.do1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
-
id: 201936068
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 144, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.b1', '18.c1', '18.e1', '18.i1', '18.j1', '18.k1', '18.l1', '18.m1', '18.n1', '18.o1', '18.p1', '18.q1', '18.t1', '18.v1', '27.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085385, 1862886, 2951738, 647, 1967536007, 2588323, 526, 38480884412], 'label': '3456.oc.9.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936069
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '48.dp1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.cf1', '16.g1'], 'contains': ['96.bh1', '144.fq1', '144.fs1', '144.ft1', '192.y1'], 'core': '864.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [37882213052, 604926858, 1968991665, 2588323, 1863007], 'label': '3456.oc.48.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.dp1', 'old_label': '48.dp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dp1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
-
id: 201936070
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.dq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1', '24.cu1', '24.dd1', '24.dl1', '24.dt1'], 'contains': ['96.y1', '96.bf1', '144.fu1', '144.fv1'], 'core': '384.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2588071, 1969714258, 1863259, 604928551, 38480884412], 'label': '3456.oc.48.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dq1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936071
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '48.dr1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '64.226', 'aut_weyl_index': 648, 'centralizer': '48.dr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.z1', '24.cs1', '24.cv1', '24.dg1', '24.dl1', '24.dm1', '24.dq1', '24.du1'], 'contains': ['96.z1', '96.bf1', '144.fw1', '144.ga1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2951738, 1863007], 'label': '3456.oc.48.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936072
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '48.ds1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '24.ba1', '24.cq1', '24.cu1', '24.cv1', '24.cw1', '24.dh1', '24.dk2', '24.dn1', '24.ds1', '24.dv1'], 'contains': ['96.ba1', '96.bf1', '144.fx1', '144.fy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1863007, 13415398178], 'label': '3456.oc.48.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.ds1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ds1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936073
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.dt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8399', 'aut_weyl_index': 72, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.ba1', '24.ct1', '24.cw1', '24.dg1', '24.dj1', '24.dm1', '24.dt1', '24.dw1'], 'contains': ['96.bb1', '96.bf1', '144.fz1', '144.gb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604928551, 1863259, 38480884412, 2588071, 1968991665], 'label': '3456.oc.48.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.dt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dt1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936074
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '48.du1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.c1', '24.bc1', '24.do1', '24.dp1', '24.dq1', '24.dr1', '24.ds1', '24.dt1', '24.du1', '24.dv1', '24.dw1'], 'contains': ['96.b1', '96.o1', '96.bc1', '96.bf1', '144.gc1', '144.gd1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [38480884129, 526, 1862886, 2588323, 604203618], 'label': '3456.oc.48.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '48.du1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.du1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936075
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.dv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.bd1', '24.bo1', '24.ci1', '24.cj1'], 'contains': ['96.bi1', '96.bl1', '96.bn1', '96.bv1', '96.ci1', '144.ge1', '144.gg1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 1969352442, 604203366], 'label': '3456.oc.48.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936076
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '48.dw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bg1', '24.bm1', '24.ci1', '24.ck1', '24.ea1'], 'contains': ['96.bi1', '96.bk1', '96.bw1', '96.by1', '96.cf1', '144.gh1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085646, 38481612726, 1862886, 1967535360, 604203366], 'label': '3456.oc.48.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936077
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.dx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.bm1', '24.cj1', '24.cl1', '24.eb1'], 'contains': ['96.bi1', '96.bm1', '96.bv1', '96.ca1', '96.cj1', '144.gi1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 38481612726, 13412085385, 1862886, 604203366], 'label': '3456.oc.48.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936078
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.dx2', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '24.bd1', '24.bm1', '24.bq1', '24.cj1'], 'contains': ['96.bj1', '96.bl1', '96.bm1', '96.bv1', '96.bw1', '144.gf1', '144.gl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 38481612726, 13414673070, 1862886, 604203366], 'label': '3456.oc.48.dx2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dx2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dx2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936079
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '576.a1', 'complements': ['288.dh1', '288.dl1', '288.di1', '288.dm1', '288.o1', '288.cy1', '288.q1', '288.db1', '288.dk1', '288.dp1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.h1', '6.k1'], 'contains': ['24.b1', '36.a1', '36.o1', '48.n1', '48.t1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 13412085385, 39799592190, 526, 647, 1862886, 2588323], 'label': '3456.oc.12.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.b1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201936080
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.dy1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.i1', '24.q1', '24.bo1', '24.bq1', '24.cj1', '24.ck1', '24.eb1'], 'contains': ['96.bi1', '96.bj1', '96.bn1', '96.bv1', '96.bz1', '96.bz2', '144.gj1', '144.gm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38481612726, 13412085385, 1862886, 1969352442, 604203366], 'label': '3456.oc.48.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dy1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936081
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.dz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '24.p1', '24.bq1', '24.cl1', '24.ea1'], 'contains': ['96.bi1', '96.bj1', '96.bo1', '96.bw1', '96.ca1', '144.gk1', '144.gn1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 38481612726, 1862886, 1969352190, 604203366], 'label': '3456.oc.48.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.dz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.dz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936082
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.ea1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bj1', '24.bm1', '24.br1', '24.ck1', '24.ea1'], 'contains': ['96.bj1', '96.bk1', '96.by1', '96.ca1', '144.go1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38481612726, 1862886, 13414673191, 1967535360, 604203366], 'label': '3456.oc.48.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ea1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ea1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936083
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.eb1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.q1', '24.bq1', '24.br1', '24.cl1', '24.eb1'], 'contains': ['96.bj1', '96.bm1', '96.bz1', '96.bz2', '96.ca1', '144.gp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1967536007, 38481612726, 1862886, 13414673322, 604203366], 'label': '3456.oc.48.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.eb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936084
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.ec1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1', '24.bm1', '24.ci1'], 'contains': ['96.bk1', '96.bl1', '96.cf1', '96.cj1', '144.gq1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 1967535360, 604203366], 'label': '3456.oc.48.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ec1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ec1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936085
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.ed1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '24.bd1', '24.cm1', '24.ea1', '24.eb1'], 'contains': ['96.bi1', '96.bj1', '96.br1', '144.gr1', '144.gs1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 38480883894, 13412085385, 1862886, 604203366], 'label': '3456.oc.48.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.ed1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ed1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936086
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '48.ee1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.bu1', '16.h1', '24.bf1'], 'contains': ['96.bp1', '144.gt1', '144.gu1', '192.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [2587950, 38480883894, 1967901282, 1862886, 1137042], 'label': '3456.oc.48.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bf1', 'old_label': '48.ee1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ee1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
-
id: 201936087
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '48.ef1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bv1', '16.h1'], 'contains': ['96.bs1', '144.gt1', '144.gv1', '192.j1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [37882212534, 2587950, 1967901282, 1862886, 1137042], 'label': '3456.oc.48.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.ef1', 'old_label': '48.ef1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ef1', 'subgroup_fusion': None, 'weyl_group': '72.44'}
-
id: 201936088
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '48.eg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1', '24.bl1', '24.cn1', '24.ea1'], 'contains': ['96.bk1', '96.bo1', '96.br1', '144.gu1', '144.gv1'], 'core': '192.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886, 1969352190, 604203366], 'label': '3456.oc.48.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '48.eg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eg1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
-
id: 201936089
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.eh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1', '24.cn1', '24.co1', '24.eb1'], 'contains': ['96.bm1', '96.bn1', '96.br1', '144.gw1', '144.gx1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 1967536007, 38480883894, 1862886, 604203366], 'label': '3456.oc.48.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '48.eh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.eh1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936090
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '432.759', 'aut_weyl_index': 96, 'centralizer': '72.a1', 'complements': ['288.df1', '288.f1', '288.i1', '288.j1', '288.dg1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.b1', '6.g1', '6.j1'], 'contains': ['24.c1', '24.r1', '24.bc1', '24.cm1', '24.do1', '36.a1', '36.n1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [13412085385, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.12.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.b1'], 'normal_contains': ['24.c1', '36.a1', '48.a1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936091
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '48.ei1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bh1', '24.ca1'], 'contains': ['96.bu1', '96.bx1', '96.by1', '96.ce1', '96.cg1', '144.gy1'], 'core': '192.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652, 13413219813, 1967535360], 'label': '3456.oc.48.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '48.ei1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ei1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936092
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '48.ej1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '24.ca1'], 'contains': ['96.bu1', '96.bx1', '96.bz2', '96.ch1', '96.ck1', '144.gz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 1968627247, 38480520960, 2226652, 13414673322], 'label': '3456.oc.48.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '48.ej1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ej1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936093
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.a1', '18.i1', '27.a1'], 'contains': ['108.d1', '108.f1', '108.g1', '108.j1', '108.k1', '108.y1', '108.z1', '108.bb1', '108.bd1', '108.bk1', '108.bl1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 13412085385, 526, 2951391], 'label': '3456.oc.54.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936094
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.b1', '18.j1', '27.a1'], 'contains': ['108.e1', '108.f1', '108.h1', '108.i1', '108.k1', '108.z1', '108.ba1', '108.bc1', '108.be1', '108.bl1', '108.bm1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 2951738, 13412085385, 526], 'label': '3456.oc.54.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936129
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.d1', '24.d1', '24.u1', '36.q1'], 'contains': ['144.l1', '144.fg1', '144.fm1', '216.o1', '288.f1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '72.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936095
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '18.d1', '18.k1', '27.a1'], 'contains': ['108.g1', '108.i1', '108.l1', '108.bb1', '108.bc1', '108.bo1', '108.bp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2951738, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.54.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936096
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.e1', '18.f1', '18.g1', '18.l1', '27.a1'], 'contains': ['108.h1', '108.j1', '108.l1', '108.bd1', '108.be1', '108.bp1', '108.bq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.54.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936097
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.m1', '27.a1'], 'contains': ['108.a1', '108.c1', '108.d1', '108.e1', '108.g1', '108.h1', '108.m1', '108.o1', '108.p1', '108.q1', '108.r1', '108.s1', '108.u1', '108.v1', '108.w1', '108.bg1', '108.bh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1968627499, 526, 13413948127, 2951391], 'label': '3456.oc.54.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936098
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.n1', '27.a1'], 'contains': ['108.f1', '108.i1', '108.j1', '108.q1', '108.r1', '108.x1', '108.bi1', '108.bj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 1968627499, 526, 13413948127], 'label': '3456.oc.54.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936099
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '18.o1', '27.a1'], 'contains': ['108.b1', '108.k1', '108.l1', '108.n1', '108.r1', '108.t1', '108.bf1', '108.bn1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967536007, 13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.54.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936100
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.p1', '27.a1'], 'contains': ['108.v1', '108.x1', '108.y1', '108.ba1', '108.bb1', '108.be1', '108.bf1', '108.bg1', '108.bj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 13412085385, 1968627499, 526, 2951391], 'label': '3456.oc.54.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936101
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2592.fs', 'aut_weyl_index': 16, 'centralizer': '216.a1', 'complements': ['288.f1', '288.i1', '288.j1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.b1', '6.s1', '6.t1'], 'contains': ['24.c1', '24.cn1', '24.co1', '24.dp1', '24.dr1', '36.co1', '36.cp1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1967536007, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.12.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': ['4.b1', '6.b1'], 'normal_contains': ['24.c1', '48.b1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 201936102
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.q1', '27.a1'], 'contains': ['108.w1', '108.x1', '108.z1', '108.bc1', '108.bd1', '108.bf1', '108.bh1', '108.bi1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 13412085385, 1968627499, 526], 'label': '3456.oc.54.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936103
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1', '18.t1', '18.u1', '27.a1'], 'contains': ['108.bg1', '108.bi1', '108.bk1', '108.bm1', '108.bn1', '108.bo1', '108.bq1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1967536007, 2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.54.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936104
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.226', 'aut_weyl_index': 432, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1', '18.v1', '27.a1'], 'contains': ['108.bh1', '108.bj1', '108.bl1', '108.bn1', '108.bp1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1967536007, 526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.54.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936105
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '16.b1', '32.a1', '32.b1', '32.c1'], 'contains': ['128.a1', '192.a1', '192.c1', '192.d1', '192.e1'], 'core': '192.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [602743680, 1137421, 38480520960, 13412085120], 'label': '3456.oc.64.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '64.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936106
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1', '16.h1', '32.c1', '32.f1', '32.g1'], 'contains': ['128.a1', '192.b1', '192.i1', '192.j1'], 'core': '192.b1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1967901282, 1137042, 38480520960], 'label': '3456.oc.64.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '64.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201936107
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1', '32.a1', '32.f1'], 'contains': ['128.a1', '192.k1', '192.l1', '192.m1'], 'core': '384.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1137042, 38480520960, 2226652], 'label': '3456.oc.64.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '64.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936108
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '32.a1', '32.b1', '32.g1'], 'contains': ['128.a1', '192.p1', '192.q1', '192.r1', '192.s1'], 'core': '384.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [602743680, 13414311772, 1137042, 38480520960], 'label': '3456.oc.64.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '64.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936109
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1', '32.b1', '32.f1'], 'contains': ['128.a1', '192.u1', '192.v1', '192.w1', '192.x1', '192.y1'], 'core': '384.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1137042, 38480520960, 1970078819], 'label': '3456.oc.64.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '64.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
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id: 201936110
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '12.b1', 'complements': ['48.x1'], 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.c1', '24.dx1', '36.a1', '36.n1', '36.co1', '36.cq1', '36.cs1', '36.ct1', '36.cw1'], 'contains': ['144.ev1', '144.gc1', '216.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.72.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': ['24.b1', '24.c1', '36.a1'], 'normal_contains': ['216.a1', '288.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936111
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '72.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '96.a1', 'complements': ['48.ei1', '48.ej1', '48.w1', '48.ba1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '24.dy1', '36.b1', '36.o1', '36.cn1', '36.cu1', '36.cy1'], 'contains': ['216.a1', '288.by1', '288.cr1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1137421, 526, 647, 1862886, 2588323], 'label': '3456.oc.72.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1', 'normal_contained_in': ['24.b1', '36.b1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
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id: 201936130
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.e1', '24.x1', '36.e1', '36.j1', '36.be1'], 'contains': ['144.e1', '144.g1', '144.k1', '144.cj1', '144.ck1', '144.fl1', '144.fp1', '216.q1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936112
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '192.a1', 'complements': ['288.r1', '288.dd2', '288.d1', '288.dc1', '288.n1', '288.dj1', '288.cw1', '288.dn1', '288.g1', '288.do1', '288.cv1', '288.de1', '288.cz1', '288.dd1', '288.da1', '288.p1', '288.db1', '288.q1', '288.cx1', '288.h1', '288.j1', '288.dk1', '288.dp1'], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.a1', '6.c1', '6.p1'], 'contains': ['24.b1', '36.b1', '36.cq1', '48.dd1'], 'core': '12.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 2951738, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.12.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': ['4.c1', '6.a1'], 'normal_contains': ['24.b1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.d1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201936113
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '36.c1', '36.i1', '36.bc1'], 'contains': ['144.b1', '144.c1', '144.f1', '144.bt1', '144.bz1', '144.dl1', '144.dt1', '216.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 13412085385, 38481612847, 1862886, 2226652], 'label': '3456.oc.72.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936114
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '36.c1', '36.j1', '36.bc1'], 'contains': ['144.b1', '144.e1', '144.g1', '144.ca1', '144.cb1', '144.du1', '144.dv1', '216.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 526, 1968991665, 1134054, 13413219692], 'label': '3456.oc.72.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936115
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '36.d1', '36.m1', '36.bd1'], 'contains': ['144.b1', '144.h1', '144.n1', '144.o1', '144.p1', '144.bp1', '144.bv1', '144.cn1', '144.ge1', '144.gi1', '144.gn1', '216.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 1967536007, 526, 1862886, 38481612978], 'label': '3456.oc.72.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936116
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '36.c1', '36.d1', '36.bh1'], 'contains': ['144.b1', '144.i1', '144.i2', '144.o1', '144.bq1', '144.bx1', '144.cu1', '144.cu2', '144.gm1', '216.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 1969352563, 526, 1862886, 38481612978], 'label': '3456.oc.72.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936117
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '36.e1', '36.f1', '36.bc1'], 'contains': ['144.c1', '144.d1', '144.g1', '144.dm1', '144.dr1', '144.dw1', '144.eh1', '216.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2226652, 38480884533, 13412085120], 'label': '3456.oc.72.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936118
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '36.e1', '36.g1', '36.bc1'], 'contains': ['144.d1', '144.e1', '144.f1', '144.dx1', '144.dy1', '144.ei1', '144.ej1', '216.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738, 38480884533, 13412085120], 'label': '3456.oc.72.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936119
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '36.c1', '36.f1', '36.be1'], 'contains': ['144.c1', '144.g1', '144.i1', '144.ct1', '144.cw1', '144.dp1', '144.dz1', '216.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 1968627378, 38480884533, 13412085120], 'label': '3456.oc.72.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936120
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '36.c1', '36.e1', '36.bf1'], 'contains': ['144.c1', '144.e1', '144.i2', '144.t1', '144.cs1', '144.cv1', '144.dn1', '144.eb1', '144.gz1', '216.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2226652, 38480884533, 13412085120], 'label': '3456.oc.72.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936121
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.n1', '36.c1', '36.g1', '36.be1'], 'contains': ['144.e1', '144.f1', '144.i1', '144.cx1', '144.cy1', '144.ea1', '144.ec1', '216.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 1968627378, 38480884533, 13412085120], 'label': '3456.oc.72.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936122
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.o1', '36.c1', '36.e1', '36.bg1'], 'contains': ['144.f1', '144.g1', '144.i2', '144.cz1', '144.da1', '144.ee1', '144.ef1', '216.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738, 38480884533, 13412085120], 'label': '3456.oc.72.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936123
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '576.a1', 'complements': ['288.r1', '288.dc1', '288.dd2', '288.n1', '288.d1', '288.de1', '288.cw1', '288.dd1', '288.cv1', '288.dj1', '288.da1', '288.cz1', '288.do1', '288.dn1', '288.p1', '288.g1', '288.cx1', '288.h1', '288.j1', '288.cy1', '288.o1', '288.dh1', '288.dl1', '288.di1', '288.dm1'], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.a1', '6.d1', '6.r1'], 'contains': ['24.b1', '36.ct1', '36.cu1', '36.cv1', '48.dk1'], 'core': '12.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 39799592190, 526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.12.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.b1'], 'normalizer': '1.a1', 'old_label': '12.e1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201936124
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '36.m1', '36.bd1'], 'contains': ['144.d1', '144.h1', '144.j1', '144.n1', '144.p1', '144.cd1', '144.cq1', '144.en1', '144.er1', '144.gf1', '144.gk1', '216.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1862886, 2588323, 38480884533, 13412085120], 'label': '3456.oc.72.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936125
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '36.d1', '36.m1', '36.bh1'], 'contains': ['144.h1', '144.i1', '144.i2', '144.j1', '144.n1', '144.o1', '144.cp1', '144.cp2', '144.db1', '144.db2', '144.eo1', '144.et1', '144.gj1', '144.gp1', '216.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967535625, 1862886, 2588323, 38480884533, 13412085120], 'label': '3456.oc.72.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936126
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '36.d1', '36.n1', '36.bd1'], 'contains': ['144.b1', '144.j1', '144.q1', '144.bn1', '144.el1', '144.ev1', '144.gr1', '216.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 2587950, 38480884412, 526, 1862886], 'label': '3456.oc.72.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936127
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.d1', '24.s1', '36.e1', '36.i1', '36.be1'], 'contains': ['144.c1', '144.f1', '144.k1', '144.cf1', '144.ch1', '144.fc1', '144.fj1', '216.o1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936128
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.f1', '36.i1', '36.bf1'], 'contains': ['144.c1', '144.k2', '144.ce1', '144.fe1', '144.fk1', '216.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38482338042, 2588202, 2226652, 1863007, 13413948127], 'label': '3456.oc.72.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936131
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.f1', '24.e1', '24.v1', '36.q1'], 'contains': ['144.l1', '144.fm1', '144.fr1', '216.q1', '288.i1'], 'core': '864.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1137421, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '72.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936132
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['18.g1', '24.e1', '24.w1'], 'contains': ['144.m1', '144.fn1', '144.fs1', '216.q1', '288.j1'], 'core': '864.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [38482336681, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.u1', 'old_label': '72.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936133
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '36.g1', '36.j1', '36.bf1'], 'contains': ['144.e1', '144.k2', '144.ci1', '144.fo1', '144.fu1', '216.r1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38480884412, 2588071, 1969714258, 13413219692], 'label': '3456.oc.72.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936134
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.c1', '6.d1', '6.k1'], 'contains': ['24.b1', '36.n1', '36.o1', '36.p1', '48.c1', '48.d1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 13412085385, 38480884412, 526, 647, 1862886, 2588323], 'label': '3456.oc.12.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
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id: 201936135
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '36.g1', '36.h1', '36.i1', '36.k1', '36.bg1'], 'contains': ['144.f1', '144.k2', '144.cl1', '144.fw1', '144.fx1', '216.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 2951738, 1863007, 13413948127], 'label': '3456.oc.72.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936136
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ba1', '36.f1', '36.h1', '36.j1', '36.l1', '36.bg1'], 'contains': ['144.g1', '144.k2', '144.cm1', '144.fy1', '144.fz1', '216.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38480884412, 2588071, 1968991665, 13413219692], 'label': '3456.oc.72.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936137
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb1', '36.e1', '36.m1', '36.bh1'], 'contains': ['144.d1', '144.h1', '144.i2', '144.k1', '144.cg1', '144.cr1', '144.dd1', '144.ey1', '144.fh1', '216.u1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 38480884412, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936138
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.y2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb2', '36.f1', '36.g1', '36.h1', '36.m1', '36.bh1'], 'contains': ['144.d1', '144.h1', '144.i1', '144.k2', '144.cg2', '144.cr2', '144.dd2', '144.ey2', '144.fh2', '216.u2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 13413948258, 1967536007, 1863138, 2588323], 'label': '3456.oc.72.y2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.y2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936139
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bc1', '36.i1', '36.j1', '36.k1', '36.l1', '36.m1', '36.n1', '36.bh1'], 'contains': ['144.b1', '144.j1', '144.k1', '144.k2', '144.bo1', '144.em1', '144.ex1', '144.ex2', '144.gc1', '216.v1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38480884129, 526, 1862886, 2588323], 'label': '3456.oc.72.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936140
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bd1', '36.d1', '36.bd1'], 'contains': ['144.n1', '144.o1', '144.q1', '144.gg1', '144.gl1', '144.gs1', '144.gw1', '216.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 1967536007, 38480883894, 13414673070, 1862886], 'label': '3456.oc.72.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936141
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.h1', '24.be1', '36.q1'], 'contains': ['144.l1', '144.ez1', '216.bb1', '288.k1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2586614, 1967901282, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '72.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936142
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '24.bf1'], 'contains': ['144.r1', '144.gt1', '216.bc1', '288.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2587950, 13414673070, 1967901282, 1862886, 1137042], 'label': '3456.oc.72.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bc1', 'old_label': '72.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
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id: 201936143
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.f1', '36.r1', '36.x1', '36.bc1'], 'contains': ['144.v1', '144.w1', '144.z1', '144.bt1', '144.ca1', '144.dm1', '144.dx1', '216.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [265, 13412085385, 39797775360, 1862886, 2226652], 'label': '3456.oc.72.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '72.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936144
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.g1', '36.r1', '36.y1', '36.bc1'], 'contains': ['144.v1', '144.y1', '144.ba1', '144.bz1', '144.cb1', '144.dw1', '144.dy1', '216.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39798138294, 526, 1968991665, 1134054, 13413219692], 'label': '3456.oc.72.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936145
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '41472.kr', 'aut_weyl_index': 1, 'centralizer': '3456.a1', 'complements': ['1728.a1', '1728.d1', '1728.g1', '1728.i1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '6.p1', '6.q1', '6.s1', '8.f1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1967901282, 1862886, 2951738, 647, 38480884412, 2588323, 526, 1137421, 604203618], 'label': '3456.oc.2.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
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id: 201936146
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.l1'], 'contains': ['24.f1', '24.g1', '24.i1', '24.l1', '24.m1', '24.n1', '24.o1', '24.bn1', '24.bp1', '24.bu1', '24.bv1', '24.bw1', '24.bx1', '24.by1', '24.bz1', '36.c1', '36.r1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 1969352563, 265, 38481612847, 1862886, 2226652, 13414673322], 'label': '3456.oc.12.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201936147
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.h1', '36.s1', '36.bb1', '36.bd1'], 'contains': ['144.v1', '144.bb1', '144.bf1', '144.bg1', '144.bh1', '144.bn1', '144.bv1', '144.cd1', '144.gg1', '144.gi1', '144.gk1', '216.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 13412085385, 526, 1862886, 38481612978], 'label': '3456.oc.72.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936148
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.i1', '36.r1', '36.s1', '36.bh1'], 'contains': ['144.v1', '144.bc1', '144.bc2', '144.bg1', '144.bo1', '144.bx1', '144.cg1', '144.cg2', '144.gj1', '216.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1969352563, 526, 1862886, 13414673191, 38481612978], 'label': '3456.oc.72.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936149
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.j1', '36.t1', '36.u1', '36.bc1'], 'contains': ['144.w1', '144.x1', '144.ba1', '144.dl1', '144.dr1', '144.du1', '144.ei1', '216.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693, 2226652, 38480884533], 'label': '3456.oc.72.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936150
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.k1', '36.t1', '36.v1', '36.bc1'], 'contains': ['144.x1', '144.y1', '144.z1', '144.dt1', '144.dv1', '144.eh1', '144.ej1', '216.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693, 2951738, 38480884533], 'label': '3456.oc.72.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936151
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.l1', '36.r1', '36.u1', '36.be1'], 'contains': ['144.w1', '144.ba1', '144.bc1', '144.cf1', '144.cj1', '144.dp1', '144.ea1', '216.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 1968627378, 38480884533], 'label': '3456.oc.72.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936152
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.m1', '36.r1', '36.t1', '36.bf1'], 'contains': ['144.w1', '144.y1', '144.bc2', '144.bj1', '144.ce1', '144.ci1', '144.dn1', '144.eb1', '144.gz1', '216.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2226652, 13413948127, 38480884533], 'label': '3456.oc.72.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936153
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.n1', '36.r1', '36.v1', '36.be1'], 'contains': ['144.y1', '144.z1', '144.bc1', '144.ch1', '144.ck1', '144.dz1', '144.ec1', '216.j1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 1968627378, 38480884533], 'label': '3456.oc.72.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936154
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.o1', '36.r1', '36.t1', '36.bg1'], 'contains': ['144.z1', '144.ba1', '144.bc2', '144.cl1', '144.cm1', '144.ee1', '144.ef1', '216.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738, 13413948127, 38480884533], 'label': '3456.oc.72.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936155
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.p1', '36.bb1', '36.bd1'], 'contains': ['144.x1', '144.bb1', '144.bd1', '144.bf1', '144.bh1', '144.cn1', '144.cq1', '144.el1', '144.er1', '144.gl1', '144.gn1', '216.l1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1967536007, 1862886, 2588323, 38480884533], 'label': '3456.oc.72.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936156
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.q1', '36.s1', '36.bb1', '36.bh1'], 'contains': ['144.bb1', '144.bc1', '144.bc2', '144.bd1', '144.bf1', '144.bg1', '144.cp1', '144.cp2', '144.cr1', '144.cr2', '144.em1', '144.et1', '144.gm1', '144.gp1', '216.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085385, 1967535625, 1862886, 2588323, 38480884533], 'label': '3456.oc.72.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936157
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.162', 'aut_weyl_index': 192, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1'], 'contains': ['24.h1', '24.i1', '24.q1', '24.r1', '24.bd1', '24.bo1', '24.bq1', '24.cj1', '24.cm1', '24.co1', '24.eb1', '36.d1', '36.s1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 1967536007, 13412085385, 38480884412, 526, 1862886, 604203618], 'label': '3456.oc.12.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936158
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.r1', '36.a1', '36.s1', '36.bd1'], 'contains': ['144.v1', '144.bd1', '144.bi1', '144.bp1', '144.en1', '144.ev1', '144.gs1', '216.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13412085646, 2587950, 39799592190, 526, 1862886], 'label': '3456.oc.72.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936159
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.s1', '24.u1', '36.t1', '36.x1', '36.be1'], 'contains': ['144.a1', '144.w1', '144.z1', '144.ct1', '144.cx1', '144.fc1', '144.fl1', '216.o1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39799592563, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '72.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936160
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.t1', '36.u1', '36.x1', '36.bf1'], 'contains': ['144.w1', '144.be1', '144.cs1', '144.fe1', '144.fo1', '216.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2588202, 2226652, 39798138933, 1863007, 13413948127], 'label': '3456.oc.72.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936161
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.v1', '24.w1', '24.x1', '36.t1', '36.y1', '36.be1'], 'contains': ['144.a1', '144.y1', '144.ba1', '144.cw1', '144.cy1', '144.fj1', '144.fp1', '216.q1'], 'core': '144.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39799592563, 1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.72.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936162
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.y1', '36.v1', '36.y1', '36.bf1'], 'contains': ['144.y1', '144.be1', '144.cv1', '144.fk1', '144.fu1', '216.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2588071, 1969714258, 13413219692, 39798867499], 'label': '3456.oc.72.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936163
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '72.bu1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.z1', '36.v1', '36.w1', '36.x1', '36.z1', '36.bg1'], 'contains': ['144.z1', '144.be1', '144.cz1', '144.fw1', '144.fy1', '216.s1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 2951738, 39798138933, 1863007, 13413948127], 'label': '3456.oc.72.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936164
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ba1', '36.u1', '36.w1', '36.y1', '36.ba1', '36.bg1'], 'contains': ['144.ba1', '144.be1', '144.da1', '144.fx1', '144.fz1', '216.t1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2588071, 1968991665, 13413219692, 39798867499], 'label': '3456.oc.72.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936165
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb1', '36.t1', '36.bb1', '36.bh1'], 'contains': ['144.a1', '144.x1', '144.bb1', '144.bc2', '144.cu1', '144.db1', '144.dd2', '144.ex1', '144.fh1', '216.u1'], 'core': '144.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1967536007, 38480884412, 2588323, 1863007], 'label': '3456.oc.72.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936166
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.bw2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bb2', '36.u1', '36.v1', '36.w1', '36.bb1', '36.bh1'], 'contains': ['144.x1', '144.bb1', '144.bc1', '144.be1', '144.cu2', '144.db2', '144.dd1', '144.ex2', '144.fh2', '216.u2'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 1967536007, 1863138, 2588323, 13413948127], 'label': '3456.oc.72.bw2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bw2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936167
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bc1', '36.a1', '36.x1', '36.y1', '36.z1', '36.ba1', '36.bb1', '36.bh1'], 'contains': ['144.a1', '144.v1', '144.bd1', '144.be1', '144.bq1', '144.eo1', '144.ey1', '144.ey2', '144.gc1', '216.v1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39799592563, 13412085646, 526, 1862886, 2588323], 'label': '3456.oc.72.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936168
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.l1'], 'contains': ['24.j1', '24.k1', '24.m1', '24.o1', '24.s1', '24.x1', '24.bb1', '24.bx1', '24.bz1', '24.ce1', '24.cf1', '24.cp1', '24.cr1', '24.di1', '24.dk1', '36.e1', '36.t1'], 'core': '48.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1968627126, 604203487, 13412085385, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.12.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201936169
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bd1', '36.s1', '36.bd1'], 'contains': ['144.bf1', '144.bg1', '144.bi1', '144.ge1', '144.gf1', '144.gr1', '144.gw1', '216.w1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 2587950, 1967536007, 38480883894, 1862886], 'label': '3456.oc.72.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936170
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bg1', '36.bc1', '36.bd1', '36.bh1'], 'contains': ['144.b1', '144.d1', '144.n1', '144.v1', '144.x1', '144.bf1', '144.bk1', '144.bl1', '144.br1', '144.dg1', '144.gh1', '216.x1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 38481612978, 1967535360], 'label': '3456.oc.72.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936171
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bh1', '36.bc1', '36.be1', '36.bf1'], 'contains': ['144.c1', '144.e1', '144.t1', '144.w1', '144.y1', '144.bj1', '144.bk1', '144.bm1', '144.de1', '144.dh1', '144.gy1', '216.y1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.72.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936172
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bi1', '36.bc1', '36.be1', '36.bg1'], 'contains': ['144.f1', '144.g1', '144.z1', '144.ba1', '144.bk1', '144.di1', '144.dj1', '216.z1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.72.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936173
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bj1', '36.bd1', '36.bh1'], 'contains': ['144.h1', '144.j1', '144.o1', '144.bb1', '144.bd1', '144.bg1', '144.bk1', '144.bl1', '144.co1', '144.ep1', '144.go1', '216.ba1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 2588323, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.72.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936174
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.a1', '24.be1', '36.be1', '36.bh1'], 'contains': ['144.a1', '144.i1', '144.k1', '144.bc1', '144.bk1', '144.dc1', '144.fa1', '216.bb1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884412, 2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.72.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936175
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '72.cd2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bk1', '36.bf1', '36.bg1', '36.bh1'], 'contains': ['144.i2', '144.k2', '144.bc2', '144.be1', '144.bk1', '144.dc2', '144.fa2', '216.bb2'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 13413948258, 1863138, 2588323, 1967535360], 'label': '3456.oc.72.cd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.cd2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936176
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.bf1', '24.bl1', '36.bd1'], 'contains': ['144.p1', '144.q1', '144.bh1', '144.bi1', '144.bl1', '144.gq1', '144.gu1', '216.bc1'], 'core': '576.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1862886, 1969352190], 'label': '3456.oc.72.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '72.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
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id: 201936177
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bn1', '36.i1', '36.r1', '36.bi1'], 'contains': ['144.bo1', '144.bt1', '144.bz1', '144.ce1', '144.cf1', '144.ch1', '144.cl1', '216.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 38481612847, 1862886, 2226652, 13414673322], 'label': '3456.oc.72.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936178
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bp1', '36.j1', '36.r1', '36.bi1'], 'contains': ['144.bo1', '144.ca1', '144.cb1', '144.ci1', '144.cj1', '144.ck1', '144.cm1', '216.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 526, 1968991665, 1134054, 13413948127], 'label': '3456.oc.72.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936179
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.l1'], 'contains': ['24.j1', '24.l1', '24.t1', '24.ba1', '24.bb2', '24.bw1', '24.ce1', '24.cq1', '24.ct1', '24.dj1', '24.dk2', '36.f1', '36.u1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 13413948258, 38482338042, 2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.12.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936180
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bm1', '36.bd1', '36.bj1', '36.ca1'], 'contains': ['144.bn1', '144.bp1', '144.br1', '144.co1', '144.cq1', '144.gf1', '144.gh1', '144.gi1', '144.gl1', '144.go1', '144.gq1', '216.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [526, 1862886, 38481612978, 1967535360, 13414673322], 'label': '3456.oc.72.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936181
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bo1', '36.d1', '36.s1', '36.ca1'], 'contains': ['144.bn1', '144.bp1', '144.bx1', '144.cp1', '144.cp2', '144.ge1', '144.gg1', '144.gj1', '144.gm1', '216.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 13412085385, 526, 1862886, 38481612978], 'label': '3456.oc.72.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936182
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bq1', '36.m1', '36.s1', '36.bj1'], 'contains': ['144.bo1', '144.bp1', '144.bv1', '144.cr1', '144.cr2', '144.gf1', '144.gj1', '144.gk1', '144.gp1', '216.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 13414673191, 38481612978], 'label': '3456.oc.72.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936183
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bn1', '36.c1', '36.x1', '36.bi1'], 'contains': ['144.bq1', '144.bt1', '144.ca1', '144.cs1', '144.ct1', '144.cx1', '144.cz1', '216.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [265, 39797775360, 1862886, 2226652, 13414673322], 'label': '3456.oc.72.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '72.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936184
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bp1', '36.c1', '36.y1', '36.bi1'], 'contains': ['144.bq1', '144.bz1', '144.cb1', '144.cv1', '144.cw1', '144.cy1', '144.da1', '216.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39798138294, 526, 1968991665, 1134054, 13413948127], 'label': '3456.oc.72.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936185
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bq1', '36.d1', '36.bb1', '36.bj1'], 'contains': ['144.bn1', '144.bq1', '144.bv1', '144.db1', '144.db2', '144.gl1', '144.gm1', '144.gn1', '144.gp1', '216.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 38481612978, 13414673322], 'label': '3456.oc.72.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936186
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.br1', '36.bh1', '36.bi1', '36.bj1'], 'contains': ['144.bo1', '144.bq1', '144.br1', '144.dc1', '144.dc2', '144.dd1', '144.dd2', '144.go1', '144.gp1', '216.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [526, 1862886, 13414673191, 38481612978, 1967535360], 'label': '3456.oc.72.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936187
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bs1', '36.bc1', '36.bi1', '36.cb1'], 'contains': ['144.br1', '144.bt1', '144.cb1', '144.de1', '144.di1', '144.dr1', '144.ej1', '216.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 38481612847, 1862886, 2226652, 1967535360], 'label': '3456.oc.72.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936188
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bs1', '36.cc1'], 'contains': ['144.bs1', '144.bu1', '144.cc1', '144.df1', '144.dk1', '144.ds1', '144.ek1', '216.bj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882941487, 265, 1862886, 2226652, 1967535360], 'label': '3456.oc.72.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '72.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936189
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bt1', '36.bc1', '36.bi1', '36.cd1'], 'contains': ['144.br1', '144.bz1', '144.ca1', '144.dh1', '144.dj1', '144.eh1', '144.ei1', '216.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 38481612847, 13413586612, 1862886, 1967535360], 'label': '3456.oc.72.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936190
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.l1'], 'contains': ['24.k1', '24.n1', '24.y1', '24.z1', '24.bb2', '24.by1', '24.cf1', '24.cs1', '24.cu1', '24.dk2', '24.dl1', '36.g1', '36.v1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 13413948258, 38482338042, 2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.12.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936191
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bu1', '36.c1', '36.r1', '36.cb1'], 'contains': ['144.bt1', '144.bx1', '144.cb1', '144.dn1', '144.dp1', '144.ec1', '144.ee1', '216.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 265, 38481612847, 1862886, 2226652], 'label': '3456.oc.72.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936192
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.bu1', '36.cc1'], 'contains': ['144.bu1', '144.by1', '144.cc1', '144.do1', '144.dq1', '144.ed1', '144.eg1', '216.bl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 37882941487, 265, 1862886, 2226652], 'label': '3456.oc.72.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '72.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936193
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bv1', '36.c1', '36.r1', '36.cd1'], 'contains': ['144.bx1', '144.bz1', '144.ca1', '144.dz1', '144.ea1', '144.eb1', '144.ef1', '216.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1969352563, 265, 38481612847, 13413586612, 1862886], 'label': '3456.oc.72.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936194
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bw1', '36.f1', '36.r1', '36.bk1'], 'contains': ['144.ce1', '144.cg2', '144.cm1', '144.dm1', '144.dp1', '144.dw1', '144.dz1', '216.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 13413948127, 1968627378, 38480884533], 'label': '3456.oc.72.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936195
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bx1', '36.e1', '36.r1', '36.bl1'], 'contains': ['144.cf1', '144.cg1', '144.ck1', '144.dm1', '144.dn1', '144.dy1', '144.ef1', '216.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1968627247, 1134693, 2226652, 38480884533], 'label': '3456.oc.72.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936196
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.by1', '36.g1', '36.r1', '36.bk1'], 'contains': ['144.cg2', '144.ci1', '144.cl1', '144.dx1', '144.dy1', '144.ea1', '144.ec1', '216.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 13413948127, 1968627378, 38480884533], 'label': '3456.oc.72.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936197
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bz1', '36.e1', '36.r1', '36.bm1'], 'contains': ['144.cg1', '144.ch1', '144.cj1', '144.dw1', '144.dx1', '144.eb1', '144.ee1', '216.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1968627247, 1134693, 2951738, 38480884533], 'label': '3456.oc.72.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936198
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bw1', '36.c1', '36.u1', '36.bk1'], 'contains': ['144.cs1', '144.cu2', '144.da1', '144.dl1', '144.dp1', '144.du1', '144.ea1', '216.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 1968627378, 38480884533], 'label': '3456.oc.72.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936199
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bx1', '36.c1', '36.t1', '36.bl1'], 'contains': ['144.ct1', '144.cu1', '144.cy1', '144.dl1', '144.dn1', '144.dv1', '144.ef1', '216.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1968627247, 1134693, 2226652, 38480884533], 'label': '3456.oc.72.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936200
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.by1', '36.c1', '36.v1', '36.bk1'], 'contains': ['144.cu2', '144.cv1', '144.cz1', '144.dt1', '144.dv1', '144.dz1', '144.ec1', '216.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 1968627378, 38480884533], 'label': '3456.oc.72.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936201
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.e1', '6.f1', '6.m1'], 'contains': ['24.z1', '24.ba1', '24.bb2', '24.cv1', '24.cw1', '24.dm1', '24.dn1', '36.h1', '36.w1'], 'core': '192.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 13413948258, 38482338042, 2588202, 1967536007, 1863007, 2951391], 'label': '3456.oc.12.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936202
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.bz1', '36.c1', '36.t1', '36.bm1'], 'contains': ['144.cu1', '144.cw1', '144.cx1', '144.dt1', '144.du1', '144.eb1', '144.ee1', '216.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1968627247, 1134693, 2951738, 38480884533], 'label': '3456.oc.72.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936296
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '72.gg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dx1', '24.dy1', '24.dz1', '36.da1'], 'contains': ['216.a1', '288.ca1', '288.ct1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [37883665321, 526, 647, 1862886, 2588323], 'label': '3456.oc.72.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '72.gg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gg1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
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id: 201936203
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ca1', '36.bf1', '36.bi1', '36.bk1'], 'contains': ['144.ce1', '144.ci1', '144.cs1', '144.cv1', '144.dc2', '144.de1', '144.dh1', '144.gy1', '144.gz1', '216.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 13413948127, 1967535360, 38480884533], 'label': '3456.oc.72.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936204
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cb1', '36.be1', '36.bi1', '36.bl1'], 'contains': ['144.cf1', '144.ck1', '144.ct1', '144.cy1', '144.dc1', '144.de1', '144.dj1', '216.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.72.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936205
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cc1', '36.be1', '36.bi1', '36.bm1'], 'contains': ['144.ch1', '144.cj1', '144.cw1', '144.cx1', '144.dc1', '144.dh1', '144.di1', '216.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.72.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936206
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cd1', '36.bg1', '36.bi1', '36.bk1'], 'contains': ['144.cl1', '144.cm1', '144.cz1', '144.da1', '144.dc2', '144.di1', '144.dj1', '216.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 13413948127, 1967535360, 38480884533], 'label': '3456.oc.72.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936207
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ce1', '36.f1', '36.t1', '36.bi1'], 'contains': ['144.ce1', '144.cm1', '144.ct1', '144.cw1', '144.dd2', '144.dr1', '144.eh1', '216.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2226652, 13413948127, 38480884533], 'label': '3456.oc.72.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936208
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ce1', '36.e1', '36.u1', '36.bi1'], 'contains': ['144.cf1', '144.cj1', '144.cs1', '144.da1', '144.dd1', '144.dr1', '144.ei1', '216.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1967536007, 1134693, 2226652, 38480884533], 'label': '3456.oc.72.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936209
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cf1', '36.e1', '36.v1', '36.bi1'], 'contains': ['144.ch1', '144.ck1', '144.cv1', '144.cz1', '144.dd1', '144.eh1', '144.ej1', '216.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1967536007, 1134693, 2951738, 38480884533], 'label': '3456.oc.72.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936210
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cf1', '36.g1', '36.t1', '36.bi1'], 'contains': ['144.ci1', '144.cl1', '144.cx1', '144.cy1', '144.dd2', '144.ei1', '144.ej1', '216.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738, 13413948127, 38480884533], 'label': '3456.oc.72.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936211
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cg1', '36.bc1', '36.bk1', '36.bl1'], 'contains': ['144.de1', '144.dg1', '144.dj1', '144.dl1', '144.dm1', '144.dv1', '144.dy1', '216.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.72.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936212
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.g1', '6.l1'], 'contains': ['24.f1', '24.s1', '24.t1', '24.z1', '24.bc1', '24.bn1', '24.cp1', '24.cq1', '24.cs1', '24.dq1', '24.ds1', '36.i1', '36.x1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 602744206, 13413948127, 2951391], 'label': '3456.oc.12.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201936213
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ch1', '36.bc1', '36.bk1', '36.bm1'], 'contains': ['144.dg1', '144.dh1', '144.di1', '144.dt1', '144.du1', '144.dw1', '144.dx1', '216.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.72.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936214
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ci1', '36.bd1', '36.ca1'], 'contains': ['144.cd1', '144.cn1', '144.co1', '144.dg1', '144.el1', '144.en1', '144.ep1', '144.ge1', '144.gg1', '144.gh1', '144.gq1', '216.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323, 1967535360, 38480884533], 'label': '3456.oc.72.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936215
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cj1', '36.m1', '36.s1', '36.ca1'], 'contains': ['144.cd1', '144.cg1', '144.cg2', '144.cp1', '144.cp2', '144.cr1', '144.cr2', '144.em1', '144.en1', '144.et1', '144.ge1', '144.gf1', '144.gi1', '144.gj1', '216.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1967535625, 1862886, 2588323, 38480884533], 'label': '3456.oc.72.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936216
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cj1', '36.d1', '36.bb1', '36.ca1'], 'contains': ['144.cn1', '144.cp1', '144.cp2', '144.cu1', '144.cu2', '144.db1', '144.db2', '144.el1', '144.eo1', '144.et1', '144.gg1', '144.gi1', '144.gl1', '144.gm1', '216.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085767, 1967535625, 1862886, 2588323, 38480884533], 'label': '3456.oc.72.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.do1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936217
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.ck1', '36.bh1', '36.bj1', '36.ca1'], 'contains': ['144.co1', '144.cr1', '144.cr2', '144.db1', '144.db2', '144.dc1', '144.dc2', '144.em1', '144.eo1', '144.ep1', '144.gh1', '144.gj1', '144.gm1', '144.go1', '216.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1862886, 2588323, 1967535360, 38480884533], 'label': '3456.oc.72.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936218
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cl1', '36.m1', '36.bb1', '36.bj1'], 'contains': ['144.cq1', '144.cr1', '144.cr2', '144.db1', '144.db2', '144.dd1', '144.dd2', '144.em1', '144.eo1', '144.er1', '144.gi1', '144.gk1', '144.gn1', '144.gp1', '216.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967536007, 13412085385, 1862886, 2588323, 38480884533], 'label': '3456.oc.72.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936219
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cm1', '36.n1', '36.s1', '36.bj1'], 'contains': ['144.bn1', '144.bo1', '144.em1', '144.ev1', '144.gr1', '216.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 13412085385, 38480884412, 526, 1862886], 'label': '3456.oc.72.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936220
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cm1', '36.a1', '36.d1', '36.bj1'], 'contains': ['144.bp1', '144.bq1', '144.eo1', '144.ev1', '144.gs1', '216.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 13412085385, 39799592190, 526, 1862886], 'label': '3456.oc.72.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '72.ds1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936221
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cn1', '36.bd1', '36.bj1', '36.co1'], 'contains': ['144.br1', '144.bv1', '144.ep1', '144.er1', '144.ev1', '144.gu1', '144.gw1', '216.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 38480884412, 526, 1862886, 1967535360], 'label': '3456.oc.72.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936222
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cn1', '36.cp1'], 'contains': ['144.bs1', '144.bw1', '144.eq1', '144.es1', '144.ew1', '144.gv1', '144.gx1', '216.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882213052, 2587950, 526, 1862886, 1967535360], 'label': '3456.oc.72.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.du1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936223
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.j1', '6.l1'], 'contains': ['24.g1', '24.x1', '24.y1', '24.ba1', '24.bc1', '24.bp1', '24.cr1', '24.ct1', '24.cu1', '24.ds1', '24.dt1', '36.j1', '36.y1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38480884412, 526, 1968991665, 2588323, 602744206, 13413948127], 'label': '3456.oc.12.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936224
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.co1', '36.d1', '36.s1', '36.co1'], 'contains': ['144.bv1', '144.bx1', '144.et1', '144.ev1', '144.gw1', '216.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 1967536007, 38480884412, 526, 1862886], 'label': '3456.oc.72.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.dv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936225
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.dw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.co1', '36.cp1'], 'contains': ['144.bw1', '144.by1', '144.eu1', '144.ew1', '144.gx1', '216.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882213052, 2587950, 1967536007, 526, 1862886], 'label': '3456.oc.72.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '72.dw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936226
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.dx1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cp1', '36.i1', '36.t1', '36.bk1'], 'contains': ['144.ce1', '144.cl1', '144.dl1', '144.dt1', '144.ex1', '144.fc1', '144.fj1', '216.cg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.72.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.dx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936227
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.dy1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cq1', '36.i1', '36.u1', '36.bl1', '36.bo1', '36.bs1'], 'contains': ['144.cf1', '144.dl1', '144.ex2', '144.fe1', '144.fx1', '216.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 13412085385, 2226652, 1863007], 'label': '3456.oc.72.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.dy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936228
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.dz1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cs1', '36.i1', '36.v1', '36.bm1', '36.bp1', '36.bt1'], 'contains': ['144.ch1', '144.dt1', '144.ex2', '144.fk1', '144.fw1', '216.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 13412085385, 2226275, 1863007], 'label': '3456.oc.72.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.dz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936229
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ea1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cr1', '36.j1', '36.t1', '36.bk1'], 'contains': ['144.ci1', '144.cm1', '144.du1', '144.dv1', '144.ex1', '144.fl1', '144.fp1', '216.ci1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.72.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.ea1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ea1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936230
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.eb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ct1', '36.j1', '36.u1', '36.bm1', '36.bq1', '36.bu1'], 'contains': ['144.cj1', '144.du1', '144.ex2', '144.fo1', '144.fz1', '216.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 38480884412, 2588071], 'label': '3456.oc.72.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.eb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936231
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ec1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '36.j1', '36.v1', '36.bl1', '36.br1', '36.bv1'], 'contains': ['144.ck1', '144.dv1', '144.ex2', '144.fu1', '144.fy1', '216.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 13412085385, 38480884412, 2588071, 1969714258], 'label': '3456.oc.72.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ec1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ec1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936232
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.ed1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cv1', '36.k1', '36.w1', '36.bn1', '36.bq1', '36.br1', '36.bs1', '36.bt1'], 'contains': ['144.ex2', '144.fw1', '144.fx1', '216.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 2951738, 13412085385, 1863007], 'label': '3456.oc.72.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ed1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ed1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936233
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ee1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cw1', '36.l1', '36.w1', '36.bn1', '36.bo1', '36.bp1', '36.bu1', '36.bv1'], 'contains': ['144.ex2', '144.fy1', '144.fz1', '216.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 13412085385, 38480884412, 2588071, 1968991665], 'label': '3456.oc.72.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ee1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ee1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936234
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.g1', '6.m1'], 'contains': ['24.z1', '24.bc1', '24.cv1', '24.du1', '24.dv1', '36.k1', '36.z1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 526, 602744206, 13413948127], 'label': '3456.oc.12.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
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id: 201936235
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.ef1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cp1', '36.e1', '36.x1', '36.bk1'], 'contains': ['144.cs1', '144.cz1', '144.dm1', '144.dx1', '144.ey1', '144.fc1', '144.fl1', '216.cg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39799592563, 13412085385, 2226652, 2588323, 1863007], 'label': '3456.oc.72.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '72.ef1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ef1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936236
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.eg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cq1', '36.f1', '36.x1', '36.bl1', '36.bo1', '36.bw1'], 'contains': ['144.ct1', '144.dm1', '144.ey2', '144.fe1', '144.fy1', '216.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 13412085385, 2226652, 39798138933, 1863007], 'label': '3456.oc.72.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.eg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936237
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.eh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cr1', '36.e1', '36.y1', '36.bk1'], 'contains': ['144.cv1', '144.da1', '144.dw1', '144.dy1', '144.ey1', '144.fj1', '144.fp1', '216.ci1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [39799592563, 13412085646, 1968991665, 2588323, 1863007], 'label': '3456.oc.72.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.eh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936238
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ei1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ct1', '36.f1', '36.y1', '36.bm1', '36.bp1', '36.bx1'], 'contains': ['144.cw1', '144.dw1', '144.ey2', '144.fk1', '144.fz1', '216.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 2588071, 39798867499], 'label': '3456.oc.72.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ei1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ei1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936239
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.ej1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cs1', '36.g1', '36.x1', '36.bm1', '36.bq1', '36.by1'], 'contains': ['144.cx1', '144.dx1', '144.ey2', '144.fo1', '144.fw1', '216.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 13412085385, 2226275, 39798138933, 1863007], 'label': '3456.oc.72.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ej1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ej1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936240
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ek1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cu1', '36.g1', '36.y1', '36.bl1', '36.br1', '36.bz1'], 'contains': ['144.cy1', '144.dy1', '144.ey2', '144.fu1', '144.fx1', '216.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 13412085385, 2588071, 1969714258, 39798867499], 'label': '3456.oc.72.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ek1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ek1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936241
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.el1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cv1', '36.h1', '36.z1', '36.bn1', '36.bp1', '36.br1', '36.bw1', '36.by1'], 'contains': ['144.ey2', '144.fw1', '144.fy1', '216.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2588202, 2951738, 13412085385, 39798138933, 1863007], 'label': '3456.oc.72.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.el1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.el1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936242
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.em1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cw1', '36.h1', '36.ba1', '36.bn1', '36.bo1', '36.bq1', '36.bx1', '36.bz1'], 'contains': ['144.ey2', '144.fx1', '144.fz1', '216.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 13412085385, 2588071, 1968991665, 39798867499], 'label': '3456.oc.72.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.em1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.em1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936243
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.en1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cx1', '36.bh1', '36.bk1', '36.ca1'], 'contains': ['144.cg2', '144.co1', '144.cp1', '144.cu2', '144.dc2', '144.dg1', '144.ex1', '144.ey1', '144.fa1', '216.co1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38480884412, 2588323, 1863007, 1967535360], 'label': '3456.oc.72.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.en1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936244
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.en2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cx2', '36.bh1', '36.bl1', '36.bm1', '36.bn1', '36.ca1'], 'contains': ['144.cg1', '144.co1', '144.cp2', '144.cu1', '144.dc1', '144.dg1', '144.ex2', '144.ey2', '144.fa2', '216.co2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 38480884129, 1863138, 2588323, 1967535360], 'label': '3456.oc.72.en2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.en2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.en2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936245
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.j1', '6.m1'], 'contains': ['24.ba1', '24.bc1', '24.cw1', '24.dv1', '24.dw1', '36.l1', '36.ba1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 1968991316, 38480884412, 526, 2588323, 602744206, 13413948127], 'label': '3456.oc.12.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936246
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.eo1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.cy1', '36.m1', '36.bb1', '36.bo1', '36.bp1', '36.bq1', '36.br1', '36.ca1'], 'contains': ['144.cd1', '144.cn1', '144.cp1', '144.cq1', '144.cr1', '144.db1', '144.ex2', '144.ey2', '144.fh2', '216.cp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884129, 1967536007, 13412085385, 1863138, 2588323], 'label': '3456.oc.72.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.eo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936247
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.eo2', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cy2', '36.m1', '36.bb1', '36.ca1'], 'contains': ['144.cd1', '144.cn1', '144.cp2', '144.cq1', '144.cr2', '144.db2', '144.ex1', '144.ey1', '144.fh1', '216.cp2'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 13412085385, 38480884412, 2588323, 1863007], 'label': '3456.oc.72.eo2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.eo2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eo2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936248
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ep1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.r1', '24.cz1', '24.da1', '36.q1'], 'contains': ['144.ez1', '144.fg1', '144.fr1', '216.cq1', '288.df1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2586614, 1967901282, 2226652, 2588323, 1863007], 'label': '3456.oc.72.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '72.ep1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ep1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936249
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.eq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.s1', '24.db1', '36.q1'], 'contains': ['144.ez1', '144.fm1', '216.cs1', '288.dg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2586735, 13413586612, 1967901775, 2588323, 1863007], 'label': '3456.oc.72.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '72.eq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eq1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936250
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.er1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.cz1', '24.dc1', '36.be1', '36.bk1', '36.cb1'], 'contains': ['144.de1', '144.di1', '144.dp1', '144.ec1', '144.fa1', '144.fc1', '144.fp1', '216.cq1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.72.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.er1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.er1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936251
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.es1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.da1', '24.dc1', '36.cc1'], 'contains': ['144.df1', '144.dk1', '144.dq1', '144.ed1', '144.fb1', '144.fd1', '144.fq1', '216.cq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882213052, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.72.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '72.es1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.es1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936252
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.et1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dd1', '36.bf1', '36.bl1', '36.cb1'], 'contains': ['144.de1', '144.dn1', '144.fa2', '144.fe1', '144.fu1', '216.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38482338042, 2588202, 2226652, 1863007, 1967535360], 'label': '3456.oc.72.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.et1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.et1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936253
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.eu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dd1', '36.cc1'], 'contains': ['144.df1', '144.do1', '144.fb2', '144.ff1', '144.fv1', '216.cr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 37883666682, 2226652, 1863007, 1967535360], 'label': '3456.oc.72.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.eu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.eu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936254
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ev1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.db1', '24.de1', '36.be1', '36.bk1', '36.cd1'], 'contains': ['144.dh1', '144.dj1', '144.dz1', '144.ea1', '144.fa1', '144.fj1', '144.fl1', '216.cs1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 13413586612, 2588323, 1863007, 1967535360], 'label': '3456.oc.72.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.ev1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ev1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936255
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ew1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.df1', '36.bf1', '36.bm1', '36.cd1'], 'contains': ['144.dh1', '144.eb1', '144.fa2', '144.fk1', '144.fo1', '216.ct1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413586379, 38482338042, 2588202, 1863007, 1967535360], 'label': '3456.oc.72.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ew1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ew1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936256
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '41472.kr', 'aut_weyl_index': 1, 'centralizer': '3456.a1', 'complements': ['1728.a1', '1728.d1', '1728.g1', '1728.f1', '1728.k1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '6.r1', '6.t1', '8.g1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [526, 647, 38480884412, 2588323, 13415398178, 1137421, 1862886, 1967901282, 604203618], 'label': '3456.oc.2.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
-
id: 201936257
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.192', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.b1', '6.e1', '6.f1'], 'contains': ['24.h1', '24.p1', '24.q1', '24.bb1', '24.bb2', '24.bc1', '24.bq1', '24.cj1', '24.cl1', '24.cy1', '24.cy2', '24.do1', '24.dr1', '36.m1', '36.bb1'], 'core': '48.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 1967536007, 13412085385, 526, 1862886, 2588323, 604203618], 'label': '3456.oc.12.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936258
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ex1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dg1', '36.bg1', '36.bm1', '36.bn1', '36.cb1', '36.ce1'], 'contains': ['144.di1', '144.ee1', '144.fa2', '144.fw1', '144.fz1', '216.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1863007, 2951391, 1967535360], 'label': '3456.oc.72.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ex1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ex1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936259
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ey1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dh1', '36.bg1', '36.bl1', '36.bn1', '36.cd1', '36.cf1'], 'contains': ['144.dj1', '144.ef1', '144.fa2', '144.fx1', '144.fy1', '216.cv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 13413586612, 1863007, 1967535360], 'label': '3456.oc.72.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.ey1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ey1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936260
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '72.ez1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dg1', '36.cc1', '36.cg1'], 'contains': ['144.dk1', '144.eg1', '144.fb2', '144.ga1', '144.gb1', '216.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 37883666682, 1863007, 2951391, 1967535360], 'label': '3456.oc.72.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.ez1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ez1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936261
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fa1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.di1', '36.e1', '36.t1', '36.cb1'], 'contains': ['144.dn1', '144.dr1', '144.ee1', '144.ej1', '144.fc1', '144.fh1', '144.fp1', '216.cw1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627126, 38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.72.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.fa1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fa1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936262
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.di1', '36.cc1'], 'contains': ['144.do1', '144.ds1', '144.eg1', '144.ek1', '144.fd1', '144.fi1', '144.fq1', '216.cw1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627126, 37882213052, 2226652, 2588323, 1863007], 'label': '3456.oc.72.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '72.fb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936263
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dj1', '36.f1', '36.u1', '36.bo1', '36.cb1', '36.ch1'], 'contains': ['144.dp1', '144.dr1', '144.fe1', '144.fh2', '144.fz1', '216.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.72.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fc1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936264
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dj1', '36.cc1', '36.ci1'], 'contains': ['144.dq1', '144.ds1', '144.ff1', '144.fi2', '144.gb1', '216.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 1967536007, 37883666682, 2226652, 1863007], 'label': '3456.oc.72.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.fd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936265
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fe1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dk2', '36.f1', '36.v1', '36.bp1', '36.cd1', '36.cj1'], 'contains': ['144.dz1', '144.eh1', '144.fh2', '144.fk1', '144.fy1', '216.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413586379, 38482338042, 2588202, 1967536007, 1863007], 'label': '3456.oc.72.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fe1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fe1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936266
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.ff1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dk1', '36.e1', '36.t1', '36.cd1'], 'contains': ['144.eb1', '144.ef1', '144.eh1', '144.ei1', '144.fh1', '144.fj1', '144.fl1', '216.cy2'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627126, 38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.72.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '72.ff1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ff1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936267
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dk2', '36.g1', '36.u1', '36.bq1', '36.cd1', '36.ck1'], 'contains': ['144.ea1', '144.ei1', '144.fh2', '144.fo1', '144.fx1', '216.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 1863007, 13415397945], 'label': '3456.oc.72.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fg1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936268
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.i1'], 'contains': ['24.dx1', '36.a1', '36.p1', '48.o1', '48.u1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [39799592190, 13412085385, 1862886, 604926858, 647, 526, 2588323], 'label': '3456.oc.12.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201936269
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fh1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dl1', '36.g1', '36.v1', '36.br1', '36.cb1', '36.cl1'], 'contains': ['144.ec1', '144.ej1', '144.fh2', '144.fu1', '144.fw1', '216.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.72.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fh1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936270
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fi1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dl1', '36.cc1', '36.cm1'], 'contains': ['144.ed1', '144.ek1', '144.fi2', '144.fv1', '144.ga1', '216.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 1967536007, 2951738, 37883666682, 1863007], 'label': '3456.oc.72.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.fi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fi1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936271
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.dm1', '36.h1', '36.w1', '36.bp1', '36.bq1', '36.ce1', '36.ch1', '36.cl1'], 'contains': ['144.fh2', '144.fw1', '144.fz1', '216.da1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 2226275, 1863007], 'label': '3456.oc.72.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fj1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936272
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.dn1', '36.h1', '36.w1', '36.bo1', '36.br1', '36.cf1', '36.cj1', '36.ck1'], 'contains': ['144.fh2', '144.fx1', '144.fy1', '216.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38482338042, 2588202, 1967536007, 1863007, 13415398178], 'label': '3456.oc.72.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fk1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936273
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.51', 'aut_weyl_index': 864, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dm1', '36.cg1', '36.ci1', '36.cm1'], 'contains': ['144.fi2', '144.ga1', '144.gb1', '216.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2588202, 1967536007, 37883666682, 2226275, 1863007], 'label': '3456.oc.72.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.fl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fl1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936274
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.fm1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.do1', '36.n1', '36.bb1', '36.bs1', '36.bt1', '36.bu1', '36.bv1', '36.ca1'], 'contains': ['144.bn1', '144.el1', '144.em1', '144.ex1', '144.ex2', '144.gc1', '216.dc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 13412085385, 526, 1862886, 2588323], 'label': '3456.oc.72.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fm1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936275
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '72.fn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.do1', '36.a1', '36.m1', '36.bw1', '36.bx1', '36.by1', '36.bz1', '36.ca1'], 'contains': ['144.bp1', '144.en1', '144.eo1', '144.ey1', '144.ey2', '144.gc1', '216.dc1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39799592563, 13412085385, 526, 1862886, 2588323], 'label': '3456.oc.72.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936276
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.fo1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dp1', '36.bh1', '36.ca1', '36.cb1', '36.cd1', '36.ce1', '36.cf1', '36.co1'], 'contains': ['144.br1', '144.bx1', '144.ep1', '144.et1', '144.fa1', '144.fa2', '144.fh1', '144.fh2', '144.gc1', '216.dd1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 526, 1862886, 2588323, 1967535360], 'label': '3456.oc.72.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fo1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936277
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.fp1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dp1', '36.cc1', '36.cg1', '36.cp1'], 'contains': ['144.bs1', '144.by1', '144.eq1', '144.eu1', '144.fb1', '144.fb2', '144.fi1', '144.fi2', '144.gd1', '216.dd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [526, 1862886, 37882212769, 2588323, 1967535360], 'label': '3456.oc.72.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.fp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936278
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '72.fq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dq1', '36.i1', '36.x1', '36.bs1', '36.bw1', '36.cb1', '36.ch1', '36.cq1'], 'contains': ['144.bt1', '144.fc1', '144.fe1', '144.fw1', '144.gc1', '216.de1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 2951391], 'label': '3456.oc.72.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fq1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936279
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.a1', '4.f1'], 'contains': ['24.d1', '24.e1', '24.u1', '24.v1', '24.be1', '24.cz1', '24.db1', '36.q1', '36.be1', '48.x1'], 'core': '144.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1967901282, 1863007, 2226652, 2586614, 38480884412, 13413948127, 2588323], 'label': '3456.oc.12.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '12.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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id: 201936280
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '72.fr1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dq1', '36.cc1', '36.ci1', '36.cr1'], 'contains': ['144.bu1', '144.fd1', '144.ff1', '144.ga1', '144.gd1', '216.de1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 526, 37883666682, 2951391], 'label': '3456.oc.72.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '72.fr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fr1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936281
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.fs1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dr1', '36.m1', '36.bb1', '36.ch1', '36.cj1', '36.ck1', '36.cl1', '36.co1'], 'contains': ['144.bv1', '144.er1', '144.et1', '144.fh1', '144.fh2', '144.gc1', '216.df1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 1967536007, 526, 1862886, 2588323], 'label': '3456.oc.72.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936282
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.ft1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dr1', '36.ci1', '36.cm1', '36.cp1'], 'contains': ['144.bw1', '144.es1', '144.eu1', '144.fi1', '144.fi2', '144.gd1', '216.df1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 37882212769, 2588323], 'label': '3456.oc.72.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.ft1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ft1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936283
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.fu1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ds1', '36.i1', '36.y1', '36.bt1', '36.bx1', '36.cd1', '36.cj1', '36.cs1'], 'contains': ['144.bz1', '144.fj1', '144.fk1', '144.fx1', '144.gc1', '216.dg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 13415398178], 'label': '3456.oc.72.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fu1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936284
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.fv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.ds1', '36.j1', '36.x1', '36.bu1', '36.by1', '36.cd1', '36.ck1', '36.ct1'], 'contains': ['144.ca1', '144.fl1', '144.fo1', '144.fy1', '144.gc1', '216.dg1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 39799592190, 526, 13415398178], 'label': '3456.oc.72.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fv1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936285
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fw1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dt1', '36.j1', '36.y1', '36.bv1', '36.bz1', '36.cb1', '36.cl1', '36.cw1'], 'contains': ['144.cb1', '144.fp1', '144.fu1', '144.fz1', '144.gc1', '216.dh1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38480884412, 526, 1968991665, 2588323], 'label': '3456.oc.72.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fw1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936286
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.fx1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dt1', '36.cc1', '36.cm1', '36.cx1'], 'contains': ['144.cc1', '144.fq1', '144.fv1', '144.gb1', '144.gd1', '216.dh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 37882213052, 526, 1968991665, 2588323], 'label': '3456.oc.72.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.fx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fx1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
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id: 201936287
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '72.fy1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.du1', '36.k1', '36.z1', '36.bt1', '36.by1', '36.ce1', '36.cl1', '36.cq1'], 'contains': ['144.fw1', '144.gc1', '216.di1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 526], 'label': '3456.oc.72.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.fy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fy1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936288
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.fz1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dv1', '36.k1', '36.ba1', '36.bs1', '36.bz1', '36.cf1', '36.ck1', '36.cs1'], 'contains': ['144.fx1', '144.gc1', '216.dj1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 526, 13415397945], 'label': '3456.oc.72.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.fz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.fz1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 201936289
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '72.ga1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dv1', '36.l1', '36.z1', '36.bv1', '36.bw1', '36.cf1', '36.cj1', '36.ct1'], 'contains': ['144.fy1', '144.gc1', '216.dj1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 39799592190, 526, 13415397945], 'label': '3456.oc.72.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.ga1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ga1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936290
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1'], 'contains': ['24.f1', '24.g1', '24.j1', '24.k1', '24.bg1', '24.bh1', '24.bi1', '24.bs1', '24.bt1', '24.cg1', '24.ch1', '36.bc1'], 'core': '96.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 265, 13412085385, 38481612847, 1862886, 2226652, 1967535360], 'label': '3456.oc.12.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936291
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.gb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dw1', '36.l1', '36.ba1', '36.bu1', '36.bx1', '36.ce1', '36.ch1', '36.cw1'], 'contains': ['144.fz1', '144.gc1', '216.dk1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 1968991316, 38480884412, 526, 2588323], 'label': '3456.oc.72.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '72.gb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gb1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936292
{'ambient': '3456.oc', 'aut_centralizer_order': 72, 'aut_label': '72.gc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.du1', '36.cg1', '36.cm1', '36.cr1'], 'contains': ['144.ga1', '144.gd1', '216.di1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 526, 37883666682], 'label': '3456.oc.72.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '72.gc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gc1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 201936293
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '72.gd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '96.209', 'aut_weyl_index': 432, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dw1', '36.cg1', '36.ci1', '36.cx1'], 'contains': ['144.gb1', '144.gd1', '216.dk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 37882213052, 1968991316, 526, 2588323], 'label': '3456.oc.72.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '72.gd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gd1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
-
id: 201936294
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '72.ge1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 576, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.dy1', '24.dz1', '36.cp1', '36.cr1', '36.cx1'], 'contains': ['144.ew1', '144.gd1', '216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37882213052, 526, 647, 1862886, 2588323], 'label': '3456.oc.72.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '72.ge1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ge1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936295
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '72.gf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8654', 'aut_weyl_index': 72, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '24.dx1', '24.dz1', '36.p1', '36.cv1', '36.cz1'], 'contains': ['216.a1', '288.bz1', '288.cs1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [38482336681, 526, 647, 1862886, 2588323], 'label': '3456.oc.72.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '72.gf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gf1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 201936297
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.gh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.ea1', '36.bd1', '36.bj1'], 'contains': ['144.gh1', '144.gk1', '144.gn1', '144.go1', '144.gr1', '144.gs1', '144.gu1', '216.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886, 1969352190, 13414673322], 'label': '3456.oc.72.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.gh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936298
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '72.gi1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '18.3', 'aut_weyl_index': 2304, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.eb1', '36.d1', '36.s1', '36.bj1'], 'contains': ['144.gi1', '144.gj1', '144.gm1', '144.gp1', '144.gr1', '144.gs1', '144.gw1', '216.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2587950, 1967536007, 38480883894, 13412085385, 1862886], 'label': '3456.oc.72.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '72.gi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.gi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936299
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '36.b1', 'complements': ['36.b1', '36.cy1', '36.cz1', '36.da1', '36.cu1', '36.cv1'], 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '48.y1', '48.z1', '48.ba1'], 'contains': ['192.a1', '192.b1', '288.r1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [602743680, 38480520960, 1967535360, 13412085120], 'label': '3456.oc.96.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1', 'normal_contained_in': ['24.a1'], 'normal_contains': ['192.a1', '192.b1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '3456.oc', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.227', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936300
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '96.b1', 'aut_quo_index': 12, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '24.c1', 'complements': ['36.q1'], 'conjugacy_class_count': 3, 'contained_in': ['32.d1', '48.a1', '48.b1', '48.cx1', '48.db1', '48.df1', '48.di1', '48.dn1', '48.du1'], 'contains': ['192.f1', '288.a1', '288.bx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38480884412, 2588323, 1863007], 'label': '3456.oc.96.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': ['24.c1', '48.a1', '48.b1'], 'normal_contains': ['288.a1', '384.a1'], 'normalizer': '1.a1', 'old_label': '96.b1', 'projective_image': '3456.oc', 'quotient_action_image': '24.14', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '96.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936301
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.h1', '24.p1', '24.r1', '24.bd1', '24.bg1', '24.bj1', '24.bl1', '24.bm1', '24.ci1', '24.cn1', '24.ea1', '36.bd1'], 'core': '96.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085646, 2587950, 38480884412, 526, 1862886, 1967535360, 604203618], 'label': '3456.oc.12.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936302
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '32.a1', '48.x1'], 'contains': ['192.c1', '192.l1', '192.p1', '288.e1', '288.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137042, 38480520960, 2226652, 13412085120], 'label': '3456.oc.96.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936303
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.e1', '32.b1', '48.x1'], 'contains': ['192.c1', '192.s1', '192.u1', '288.h1', '288.i1', '288.j1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137042, 38480520960, 1970078819, 13412085120], 'label': '3456.oc.96.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936304
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.cq1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '48.e1', '48.f1', '48.g1', '48.h1', '48.i1', '48.j1', '48.k1', '48.l1', '48.l2', '48.m1', '48.p1', '48.y1'], 'contains': ['192.a1', '192.f1', '192.h1', '288.b1', '288.l1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 38480884533, 13412085120], 'label': '3456.oc.96.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936305
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.e1', '48.m1', '48.q1', '48.r1', '48.s1', '48.v1', '48.z1'], 'contains': ['192.a1', '192.g1', '192.n1', '288.c1', '288.m1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [38481612726, 1862886, 13412085120, 604203366], 'label': '3456.oc.96.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936306
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.l1', '48.l2', '48.q1', '48.r1', '48.w1', '48.y1'], 'contains': ['192.a1', '192.h1', '192.o1', '288.d1', '288.n1'], 'core': '192.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627499, 38480520960, 13412085120], 'label': '3456.oc.96.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936307
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '48.f1', '48.w1', '48.ba1'], 'contains': ['192.a1', '192.k1', '192.r1', '288.e1', '288.o1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652, 13412085120], 'label': '3456.oc.96.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936308
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.u1', '32.a1', '48.x1'], 'contains': ['192.d1', '192.l1', '192.s1', '288.f1', '288.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39797775360, 1137042, 2226652, 13412085120], 'label': '3456.oc.96.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '96.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936309
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.g1', '48.k1', '48.q1', '48.s1', '48.z1'], 'contains': ['192.a1', '192.n1', '192.t1', '288.g1', '288.p1'], 'core': '192.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [13412085767, 602743680, 1967536007, 38480520960], 'label': '3456.oc.96.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936310
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.v1', '32.b1', '48.x1'], 'contains': ['192.d1', '192.p1', '192.u1', '288.i1', '288.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [39797775360, 1137042, 1970078819, 13412085120], 'label': '3456.oc.96.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936311
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.w1', '32.b1'], 'contains': ['192.e1', '192.q1', '192.v1', '288.j1', '288.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [604927215, 39797775360, 1970078819, 13412085120], 'label': '3456.oc.96.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.l1', 'old_label': '96.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936312
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.f1', '6.l1'], 'contains': ['24.a1', '24.l1', '24.n1', '24.s1', '24.x1', '24.bh1', '24.bi1', '24.cb1', '24.cc1', '24.dc1', '24.de1', '36.be1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38480884412, 2226652, 2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.12.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936313
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '48.h1', '48.w1', '48.ba1'], 'contains': ['192.a1', '192.r1', '192.w1', '288.h1', '288.q1'], 'core': '192.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [602743680, 38480520960, 1970078819, 13412085120], 'label': '3456.oc.96.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936314
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '576.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.be1', '24.bf1', '32.c1', '48.x1'], 'contains': ['192.c1', '192.d1', '192.i1', '288.k1', '288.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1967901282, 1137042, 38480520960, 13412085120], 'label': '3456.oc.96.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936315
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.e1', '48.bb1', '48.bc1', '48.bd1', '48.be1', '48.bf1', '48.bg1', '48.bh1', '48.bi1', '48.cw1', '48.du1'], 'contains': ['192.f1', '192.g1', '288.s1', '288.t1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [526, 1862886, 38481612978, 604203618], 'label': '3456.oc.96.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936316
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.k1', '48.m1', '48.bb1', '48.bj1', '48.bk1', '48.bn3', '48.bn4', '48.bo1', '48.bv1', '48.bv2', '48.cr1', '48.cs1', '48.cx1', '48.cx2'], 'contains': ['192.f1', '192.h1', '192.n1', '288.u1', '288.w1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 1134693, 13412085385, 38480884533], 'label': '3456.oc.96.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936317
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '48.l1', '48.bc1', '48.bm1', '48.bn1', '48.bq1', '48.br1', '48.bs1', '48.bv1', '48.bw1', '48.bx1', '48.cs1', '48.cx2'], 'contains': ['192.f1', '192.h1', '288.v1', '288.x1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413948258, 602743680, 1134693, 38480884533], 'label': '3456.oc.96.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936318
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.q2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.cq1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l2', '48.p1', '48.bc1', '48.bl1', '48.bn2', '48.bp1', '48.bt1', '48.bu1', '48.bv2', '48.bw2', '48.bx1', '48.cs1', '48.cx1'], 'contains': ['192.f1', '192.h1', '288.v2', '288.x2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 13413948127, 38480884533], 'label': '3456.oc.96.q2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.q2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936319
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.b1', '48.y1', '48.bd1', '48.bk1', '48.bw1', '48.bw2', '48.by1', '48.bz1', '48.ca1', '48.cb1', '48.cc1', '48.ct1', '48.da1'], 'contains': ['192.b1', '192.f1', '192.o1', '288.y1', '288.z1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1134693, 1967535360, 38480884533], 'label': '3456.oc.96.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936320
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.f1', '48.be1', '48.bl1', '48.bm1', '48.by1', '48.cd1', '48.ce1', '48.cf1', '48.cg1', '48.db1', '48.dc1'], 'contains': ['192.f1', '192.k1', '288.ba1', '288.bb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2226652, 38480884533], 'label': '3456.oc.96.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936321
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.e1', '48.g1', '48.bj1', '48.bn1', '48.bn2', '48.bz1', '48.cd1', '48.ch1', '48.ci1', '48.cj1', '48.cr1', '48.cx1', '48.cx2'], 'contains': ['192.f1', '192.n1', '288.bc1', '288.bd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085767, 602743680, 1134693, 38480884533], 'label': '3456.oc.96.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936322
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.bf1', '48.bj1', '48.bv1', '48.bv2', '48.ct1', '48.cu1', '48.cv1', '48.df1', '48.df2'], 'contains': ['192.f1', '192.o1', '192.t1', '288.be1', '288.bf1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 1968627499, 38480884533], 'label': '3456.oc.96.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936323
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.47847', 'aut_weyl_index': 24, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1'], 'contains': ['24.m1', '24.t1', '24.y1', '24.bh1', '24.bk1', '24.ca1', '24.dd1', '24.df1', '36.bf1'], 'core': '96.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 2226652, 1863007, 13413948127, 1967535360], 'label': '3456.oc.12.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
-
id: 201936324
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.b1', '48.l1', '48.bg1', '48.bn2', '48.bn3', '48.cf1', '48.ck1', '48.cm1', '48.cv1', '48.df2'], 'contains': ['192.f1', '192.o1', '288.bg1', '288.bh1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1134693, 1968627378, 38480884533], 'label': '3456.oc.96.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936325
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.v2', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.l2', '48.bg1', '48.bn1', '48.bn4', '48.ce1', '48.cl1', '48.cn1', '48.co1', '48.cv1', '48.da1', '48.df1'], 'contains': ['192.f1', '192.o1', '288.bg2', '288.bh2'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1968627247, 1134693, 38480884533], 'label': '3456.oc.96.v2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.v2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936326
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.f1', '48.h1', '48.bh1', '48.bl1', '48.bp1', '48.bq1', '48.br1', '48.ca1', '48.ch1', '48.ci1', '48.ck1', '48.cl1', '48.cp1', '48.di1', '48.dj1'], 'contains': ['192.f1', '192.r1', '288.bi1', '288.bj1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1134693, 13414311772, 38480884533], 'label': '3456.oc.96.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936327
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.g1', '48.bd1', '48.bo1', '48.bx1', '48.cg1', '48.cp1', '48.cq1', '48.cu1', '48.df1', '48.df2'], 'contains': ['192.f1', '192.t1', '288.bk1', '288.bl1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1967536007, 1134693, 38480884533], 'label': '3456.oc.96.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936328
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.h1', '48.bi1', '48.bp1', '48.bs1', '48.by1', '48.ce1', '48.cj1', '48.cm1', '48.cq1', '48.dn1', '48.dq1'], 'contains': ['192.f1', '192.w1', '288.bm1', '288.bn1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 602743680, 1970078819, 38481613099], 'label': '3456.oc.96.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
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id: 201936329
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '48.dr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.i1', '48.be1', '48.bq1', '48.bt1', '48.cb1', '48.ch1', '48.cm1', '48.cn1', '48.cq1', '48.db1', '48.dr1'], 'contains': ['192.f1', '288.bo1', '288.bs1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1134693, 2951738, 38480884533], 'label': '3456.oc.96.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936330
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.fw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.i1', '48.j1', '48.bh1', '48.bm1', '48.bs1', '48.bt1', '48.bu1', '48.cc1', '48.cd1', '48.cj1', '48.ck1', '48.co1', '48.cp1', '48.di1', '48.ds1'], 'contains': ['192.f1', '288.bp1', '288.bq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 13415036858, 1134693, 38480884533], 'label': '3456.oc.96.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936331
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.j1', '48.bi1', '48.br1', '48.bu1', '48.cb1', '48.cf1', '48.cg1', '48.ci1', '48.cn1', '48.dn1', '48.dt1'], 'contains': ['192.f1', '288.br1', '288.bt1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 602743680, 1970078440, 38481613099], 'label': '3456.oc.96.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '96.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936332
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.m1', '48.cr1', '48.cs1', '48.ct1', '48.cu1', '48.cv1', '48.cw1', '48.du1'], 'contains': ['192.f1', '192.g1', '288.bu1', '288.bv1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1862886, 2588323, 38480884533, 604203366], 'label': '3456.oc.96.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936333
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.b1', '32.d1', '48.c1', '48.n1', '48.cy1', '48.dd1', '48.dg1', '48.dk1', '48.dl1'], 'contains': ['288.a1', '288.by1', '288.bz1', '384.b1'], 'core': '288.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [1137421, 38480884412, 2588323, 1863007], 'label': '3456.oc.96.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '96.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 201936334
{'ambient': '3456.oc', 'aut_centralizer_order': 8, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '576.8399', 'aut_weyl_index': 72, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1', '6.m1'], 'contains': ['24.o1', '24.z1', '24.ba1', '24.bi1', '24.bk1', '24.cd1', '24.dg1', '24.dh1', '36.bg1'], 'core': '96.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1863007, 13413948127, 2951391, 1967535360], 'label': '3456.oc.12.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201936335
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['24.dx1', '32.d1', '48.o1', '48.dh1', '48.dm1'], 'contains': ['288.a1', '288.bz1', '288.ca1', '384.c1'], 'core': '288.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [604926858, 38480884412, 2588323, 1863007], 'label': '3456.oc.96.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1', 'old_label': '96.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
-
id: 201936336
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '12.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1', '48.cx2', '48.da1', '48.dc1', '48.df2', '48.dj1', '48.dq1', '48.dr1', '48.ds1', '48.dt1', '48.du1'], 'contains': ['192.f1', '288.bw1', '288.bx2'], 'core': '384.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [38480884129, 1863138, 2588323, 604203618], 'label': '3456.oc.96.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936337
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dy1', '32.d1', '48.cz1', '48.de1', '48.do1'], 'contains': ['288.bx1', '288.by1', '288.ca1', '384.d1'], 'core': '864.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [37882213052, 1137421, 2588323, 1863007], 'label': '3456.oc.96.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '96.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
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id: 201936338
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.dz1', '32.d1', '48.dp1'], 'contains': ['288.bx1', '288.bz1', '288.ca1', '384.e1'], 'core': '864.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [37882213052, 604926858, 2588323, 1863007], 'label': '3456.oc.96.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1', 'old_label': '96.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936339
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.e1', '48.q1', '48.bb1', '48.cr1', '48.cs1', '48.dv1', '48.dw1', '48.dx1', '48.dy1', '48.dz1', '48.ed1'], 'contains': ['192.g1', '192.h1', '192.n1', '288.cb1', '288.cd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 13412085385, 1862886, 604203366], 'label': '3456.oc.96.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936340
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.m1', '48.r1', '48.bb1', '48.bc1', '48.cs1', '48.dx2', '48.dy1', '48.dz1', '48.ea1', '48.eb1', '48.ed1'], 'contains': ['192.g1', '192.h1', '288.cc1', '288.ce1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 13414673322, 604203366], 'label': '3456.oc.96.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936341
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1', '48.bd1', '48.ct1', '48.dw1', '48.ea1', '48.ec1', '48.eg1'], 'contains': ['192.b1', '192.g1', '192.t1', '288.cf1', '288.cg1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38481612726, 1862886, 1967535360, 604203366], 'label': '3456.oc.96.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936342
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '48.v1', '48.bb1', '48.cr1', '48.dv1', '48.dx2', '48.ec1'], 'contains': ['192.g1', '192.n1', '288.ch1', '288.ci1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 604203366], 'label': '3456.oc.96.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936343
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.q1', '48.bd1', '48.bf1', '48.cu1', '48.cv1', '48.dx1', '48.dx2', '48.eb1', '48.eh1'], 'contains': ['192.g1', '192.o1', '192.t1', '288.cj1', '288.ck1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1967536007, 38481612726, 1862886, 604203366], 'label': '3456.oc.96.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936344
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.r1', '48.bf1', '48.bg1', '48.ct1', '48.cv1', '48.dv1', '48.dy1', '48.eh1'], 'contains': ['192.g1', '192.o1', '288.cl1', '288.cm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352442, 604203366], 'label': '3456.oc.96.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936345
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.l1', '6.m1'], 'contains': ['24.a1', '24.i1', '24.q1', '24.bb1', '24.bb2', '24.bc1', '24.bg1', '24.bj1', '24.bk1', '24.br1', '24.ck1', '24.cx1', '24.cx2', '24.dp1', '36.bh1'], 'core': '24.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 38480884129, 526, 1862886, 2588323, 604203618, 1967535360], 'label': '3456.oc.12.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936346
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.186', 'aut_weyl_index': 288, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1', '48.bf1', '48.cu1', '48.dz1', '48.eg1'], 'contains': ['192.g1', '192.t1', '288.cn1', '288.co1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352190, 604203366], 'label': '3456.oc.96.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936347
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '32.e1', '48.d1', '48.t1', '48.ee1'], 'contains': ['288.cp1', '288.cr1', '288.cs1', '384.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [1137421, 2587950, 38480883894, 1862886], 'label': '3456.oc.96.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '96.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
-
id: 201936348
{'ambient': '3456.oc', 'aut_centralizer_order': 27, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.dx1', '32.e1', '48.u1'], 'contains': ['288.cp1', '288.cs1', '288.ct1', '384.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [2587950, 38480883894, 604926858, 1862886], 'label': '3456.oc.96.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '96.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
-
id: 201936349
{'ambient': '3456.oc', 'aut_centralizer_order': 432, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1', '48.v1', '48.cw1', '48.ed1', '48.eg1', '48.eh1'], 'contains': ['192.g1', '288.cp1', '288.cq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886, 604203366], 'label': '3456.oc.96.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '96.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
-
id: 201936350
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dy1', '32.e1', '48.ef1'], 'contains': ['288.cq1', '288.cr1', '288.ct1', '384.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [37882212534, 1137421, 2587950, 1862886], 'label': '3456.oc.96.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.h1', 'old_label': '96.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
-
id: 201936351
{'ambient': '3456.oc', 'aut_centralizer_order': 27, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.dz1', '32.e1'], 'contains': ['288.cq1', '288.cs1', '288.ct1', '384.e1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [37882212534, 2587950, 604926858, 1862886], 'label': '3456.oc.96.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.e1', 'old_label': '96.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201936352
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.f1', '48.w1', '48.bl1', '48.ei1', '48.ej1'], 'contains': ['192.h1', '192.k1', '192.r1', '288.cu1', '288.cy1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652, 13413948127], 'label': '3456.oc.96.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936353
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.bv1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.k1', '48.r1', '48.bj1', '48.bk1', '48.bn1', '48.bn2', '48.bn3', '48.bn4', '48.bv1', '48.bv2', '48.dv1', '48.dx1', '48.dx2', '48.dy1'], 'contains': ['192.h1', '192.n1', '192.o1', '288.cv1', '288.cz1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [13412085646, 602743680, 1968627499, 38480520960], 'label': '3456.oc.96.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bv1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936354
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '48.q1', '48.bj1', '48.bo1', '48.bv1', '48.bv2', '48.dw1', '48.dx2', '48.dz1'], 'contains': ['192.h1', '192.n1', '192.t1', '288.cw1', '288.da1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1967536007, 13414673070, 38480520960], 'label': '3456.oc.96.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936355
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.h1', '48.w1', '48.bp1', '48.ei1', '48.ej1'], 'contains': ['192.h1', '192.r1', '192.w1', '288.cx1', '288.db1'], 'core': '384.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [602743680, 38480520960, 1970078819, 13413219692], 'label': '3456.oc.96.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936356
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1'], 'contains': ['24.bn1', '24.bp1', '24.br1', '24.bs1', '24.bt1', '24.ca1', '24.cb1', '24.cc1', '24.cd1', '24.ce1', '24.cf1', '36.bi1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 265, 38481612847, 1862886, 2226652, 13414673322, 1967535360], 'label': '3456.oc.12.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201936357
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '96.by1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.y1', '48.bk1', '48.bw1', '48.bw2', '48.dw1', '48.ea1', '48.ei1'], 'contains': ['192.b1', '192.h1', '288.dc1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13413948258, 602743680, 38480520960, 1967535360], 'label': '3456.oc.96.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.by1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936358
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.bz1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.l1', '48.bn4', '48.bv2', '48.bw1', '48.dy1', '48.eb1'], 'contains': ['192.h1', '192.o1', '288.dd1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 13413219409, 1968627499, 38480520960], 'label': '3456.oc.96.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bz1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936359
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.bz2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l2', '48.bn3', '48.bv1', '48.bw2', '48.dy1', '48.eb1', '48.ej1'], 'contains': ['192.h1', '192.o1', '288.dd2'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627499, 13414673191, 38480520960], 'label': '3456.oc.96.bz2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '96.bz2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bz2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936360
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.ca1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.k1', '48.bo1', '48.bv1', '48.bv2', '48.bx1', '48.dx1', '48.dz1', '48.ea1', '48.eb1'], 'contains': ['192.h1', '192.t1', '288.de1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1967536007, 38480520960, 13413948127], 'label': '3456.oc.96.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ca1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936361
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '96.cb1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.cz1', '32.f1', '48.x1'], 'contains': ['192.i1', '192.l1', '192.u1', '288.df1', '288.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1967901282, 1137042, 38480520960, 2226652], 'label': '3456.oc.96.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936362
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '96.cc1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.da1', '32.f1'], 'contains': ['192.j1', '192.m1', '192.x1', '288.df1', '288.di1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [37881446400, 1967901282, 1137042, 2226652], 'label': '3456.oc.96.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cc1', 'old_label': '96.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cc1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936363
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '96.cd1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.db1', '32.g1', '48.x1'], 'contains': ['192.i1', '192.p1', '192.s1', '288.dg1', '288.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1967901282, 13414311772, 1137042, 38480520960], 'label': '3456.oc.96.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '96.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cd1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936364
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1', '48.ba1', '48.by1', '48.ei1'], 'contains': ['192.b1', '192.k1', '192.w1', '288.dh1', '288.di1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652, 1967535360], 'label': '3456.oc.96.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ce1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936365
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '96.cf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1', '48.bk1', '48.bz1', '48.dw1', '48.ec1'], 'contains': ['192.b1', '192.n1', '288.dj1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085646, 602743680, 38480520960, 1967535360], 'label': '3456.oc.96.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cf1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936366
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1', '48.ba1', '48.ca1', '48.ei1'], 'contains': ['192.b1', '192.r1', '288.dk1'], 'core': '192.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 13414311772, 38480520960, 1967535360], 'label': '3456.oc.96.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cg1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936367
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.c1', '6.d1', '6.h1', '6.k1', '6.p1', '6.r1', '9.a1', '9.b1', '12.s1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967901282, 13412085385, 1862886, 2951738, 647, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.3.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201936368
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1'], 'contains': ['24.bm1', '24.bq1', '24.br1', '24.ck1', '24.cl1', '24.cm1', '24.cn1', '24.ea1', '24.eb1', '36.bj1'], 'core': '192.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2587950, 13412085385, 38480884412, 526, 1862886, 1967535360, 604203618], 'label': '3456.oc.12.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936369
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.ch1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.w1', '48.by1', '48.ce1', '48.ej1'], 'contains': ['192.k1', '192.o1', '192.w1', '288.dl1', '288.dm1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1968627247, 38480520960, 2226652], 'label': '3456.oc.96.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ch1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936370
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '96.ci1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.q1', '48.bj1', '48.bn3', '48.bn4', '48.bz1', '48.dv1'], 'contains': ['192.n1', '192.o1', '288.dn1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 1968627499, 38480520960, 13413948006], 'label': '3456.oc.96.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ci1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936371
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '96.cj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '48.bj1', '48.bo1', '48.dx1', '48.ec1'], 'contains': ['192.n1', '192.t1', '288.do1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 1967536007, 13412085385, 38480520960], 'label': '3456.oc.96.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '96.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.cj1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936372
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '96.ck1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.w1', '48.ca1', '48.cl1', '48.ej1'], 'contains': ['192.o1', '192.r1', '288.dp1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [602743680, 1968627247, 13414311772, 38480520960], 'label': '3456.oc.96.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '96.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ck1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936373
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.c1', '36.r1', '54.e1'], 'contains': ['216.b1', '216.c1', '216.e1', '216.h1', '216.i1', '216.j1', '216.k1', '216.be1', '216.bg1', '216.bl1', '216.bm1', '216.bn1', '216.bo1', '216.bp1', '216.bq1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1969352563, 265, 1862886, 2226652, 13414673322], 'label': '3456.oc.108.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936374
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.s1', '54.g1'], 'contains': ['216.d1', '216.e1', '216.m1', '216.n1', '216.w1', '216.bf1', '216.bh1', '216.ca1', '216.cd1', '216.cf1', '216.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2587950, 1967536007, 13412085385, 526, 1862886], 'label': '3456.oc.108.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '108.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201936375
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.e1', '36.t1', '54.e1'], 'contains': ['216.f1', '216.g1', '216.i1', '216.k1', '216.o1', '216.q1', '216.u1', '216.bo1', '216.bq1', '216.bv1', '216.bw1', '216.cg1', '216.ci1', '216.cw1', '216.cy2'], 'core': '864.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627126, 2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.108.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936376
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.f1', '36.u1', '54.a1', '54.e1'], 'contains': ['216.f1', '216.h1', '216.p1', '216.t1', '216.u2', '216.bn1', '216.bv1', '216.ch1', '216.ck1', '216.cx1', '216.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 2588202, 1967536007, 2226652, 1863007], 'label': '3456.oc.108.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936377
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.g1', '36.v1', '54.b1', '54.e1'], 'contains': ['216.g1', '216.j1', '216.r1', '216.s1', '216.u2', '216.bp1', '216.bw1', '216.cj1', '216.cl1', '216.cy1', '216.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 2588202, 1967536007, 2951738, 1863007], 'label': '3456.oc.108.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936378
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.h1', '36.w1', '54.a1', '54.b1', '54.f1'], 'contains': ['216.s1', '216.t1', '216.u2', '216.cm1', '216.cn1', '216.da1', '216.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13413948258, 2588202, 1967536007, 2226275, 1863007], 'label': '3456.oc.108.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936379
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1'], 'contains': ['24.bw1', '24.by1', '24.ca1', '24.cd1', '24.cg1', '24.ch1', '24.cp1', '24.cr1', '24.cx1', '24.dc1', '24.de1', '36.bk1'], 'core': '48.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 13412085385, 38480884412, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.12.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '12.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1', 'subgroup_fusion': None, 'weyl_group': '144.192'}
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id: 201936380
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.i1', '36.x1', '54.a1', '54.c1', '54.e1'], 'contains': ['216.b1', '216.o1', '216.p1', '216.s1', '216.v1', '216.be1', '216.cg1', '216.ch1', '216.cj1', '216.de1', '216.dg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 526, 13413948127, 2951391], 'label': '3456.oc.108.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936381
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.j1', '36.y1', '54.b1', '54.d1', '54.e1'], 'contains': ['216.c1', '216.q1', '216.r1', '216.t1', '216.v1', '216.bg1', '216.ci1', '216.ck1', '216.cl1', '216.dg1', '216.dh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 526, 1968991665, 2588323, 13413948127], 'label': '3456.oc.108.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936382
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.k1', '36.z1', '54.b1', '54.c1', '54.f1'], 'contains': ['216.s1', '216.v1', '216.cm1', '216.di1', '216.dj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 526, 13413948127], 'label': '3456.oc.108.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936383
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.l1', '36.ba1', '54.a1', '54.d1', '54.f1'], 'contains': ['216.t1', '216.v1', '216.cn1', '216.dj1', '216.dk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 1968991316, 526, 2588323, 13413948127], 'label': '3456.oc.108.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936384
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.m1', '36.bb1', '54.a1', '54.b1', '54.g1'], 'contains': ['216.d1', '216.l1', '216.m1', '216.u1', '216.u2', '216.v1', '216.bh1', '216.ca1', '216.cc1', '216.cp1', '216.cp2', '216.dc1', '216.df1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 13412085385, 526, 1862886, 2588323], 'label': '3456.oc.108.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936385
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.n1', '36.o1', '36.p1', '54.c1', '54.d1', '54.g1'], 'contains': ['216.a1', '216.n1', '216.v1', '216.cd1', '216.dc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13412085385, 526, 647, 1862886, 2588323], 'label': '3456.oc.108.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936386
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bc1', '54.e1'], 'contains': ['216.b1', '216.c1', '216.f1', '216.g1', '216.x1', '216.y1', '216.z1', '216.bj1', '216.bk1', '216.bx1', '216.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [265, 13412085385, 1862886, 2226652, 1967535360], 'label': '3456.oc.108.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936387
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1', '54.g1'], 'contains': ['216.d1', '216.l1', '216.n1', '216.w1', '216.x1', '216.ba1', '216.bc1', '216.bd1', '216.bz1', '216.ce1', '216.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 2587950, 526, 1862886, 1967535360], 'label': '3456.oc.108.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '108.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201936388
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.q1', '36.be1', '54.e1'], 'contains': ['216.h1', '216.j1', '216.o1', '216.q1', '216.y1', '216.z1', '216.bb1', '216.bs1', '216.bt1', '216.cq1', '216.cs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2226652, 2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.108.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936389
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1', '54.e1'], 'contains': ['216.i1', '216.p1', '216.r1', '216.y1', '216.bb2', '216.br1', '216.cr1', '216.ct1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2588202, 2226652, 1863007, 13413948127, 1967535360], 'label': '3456.oc.108.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936390
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1', '6.n1'], 'contains': ['24.bx1', '24.cb1', '24.cg1', '24.cq1', '24.cu1', '24.cx2', '24.dd1', '24.dh1', '36.bl1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 604203487, 38482338042, 2588202, 2226652, 1863007, 1967535360], 'label': '3456.oc.12.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936391
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bg1', '54.e1', '54.f1'], 'contains': ['216.k1', '216.s1', '216.t1', '216.z1', '216.bb2', '216.bu1', '216.cu1', '216.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 2951738, 1863007, 13413948127, 1967535360], 'label': '3456.oc.108.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936392
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bh1', '54.e1', '54.f1', '54.g1'], 'contains': ['216.e1', '216.m1', '216.u1', '216.u2', '216.v1', '216.x1', '216.ba1', '216.bb1', '216.bb2', '216.bi1', '216.cb1', '216.co1', '216.co2', '216.dd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 2588323, 1967535360], 'label': '3456.oc.108.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936393
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bi1', '54.e1'], 'contains': ['216.be1', '216.bg1', '216.bi1', '216.bj1', '216.bk1', '216.br1', '216.bs1', '216.bt1', '216.bu1', '216.bv1', '216.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [265, 1862886, 2226652, 13414673322, 1967535360], 'label': '3456.oc.108.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936394
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1', '54.g1'], 'contains': ['216.bd1', '216.bh1', '216.bi1', '216.cb1', '216.cc1', '216.cd1', '216.ce1', '216.dl1', '216.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2587950, 13412085385, 526, 1862886, 1967535360], 'label': '3456.oc.108.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '108.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201936395
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bk1', '54.e1'], 'contains': ['216.bn1', '216.bp1', '216.br1', '216.bu1', '216.bx1', '216.by1', '216.cg1', '216.ci1', '216.co1', '216.cq1', '216.cs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085385, 2226652, 2588323, 1863007, 1967535360], 'label': '3456.oc.108.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '108.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936396
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bl1', '54.e1', '54.h1'], 'contains': ['216.bo1', '216.bs1', '216.bx1', '216.ch1', '216.cl1', '216.co2', '216.cr1', '216.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 13412085385, 2226652, 1863007, 1967535360], 'label': '3456.oc.108.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936397
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.bm1', '54.e1', '54.i1'], 'contains': ['216.bq1', '216.bt1', '216.by1', '216.cj1', '216.ck1', '216.co2', '216.ct1', '216.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [2588202, 13412085385, 2226275, 1863007, 1967535360], 'label': '3456.oc.108.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936398
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bn1', '54.f1', '54.h1', '54.i1'], 'contains': ['216.cm1', '216.cn1', '216.co2', '216.cu1', '216.cv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2588202, 2951738, 13412085385, 1863007, 1967535360], 'label': '3456.oc.108.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936399
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bo1', '54.a1', '54.h1'], 'contains': ['216.ch1', '216.cn1', '216.cp1', '216.cx1', '216.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2588202, 1967536007, 13412085385, 2226652, 1863007], 'label': '3456.oc.108.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936400
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.bp1', '36.bq1', '54.a1', '54.b1', '54.i1'], 'contains': ['216.cj1', '216.ck1', '216.cm1', '216.cn1', '216.cp1', '216.cy1', '216.da1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [2588202, 1967536007, 13412085385, 2226275, 1863007], 'label': '3456.oc.108.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936401
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1', '6.o1'], 'contains': ['24.bz1', '24.cc1', '24.ch1', '24.cs1', '24.ct1', '24.cx2', '24.df1', '24.dg1', '36.bm1'], 'core': '192.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [13412085646, 604203487, 38482338042, 2588202, 1863007, 2951391, 1967535360], 'label': '3456.oc.12.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936402
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.br1', '54.b1', '54.h1'], 'contains': ['216.cl1', '216.cm1', '216.cp1', '216.cz1', '216.db1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [2588202, 1967536007, 2951738, 13412085385, 1863007], 'label': '3456.oc.108.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936403
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bs1', '36.bw1', '54.a1', '54.c1', '54.h1'], 'contains': ['216.ch1', '216.cm1', '216.dc1', '216.de1', '216.dj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 13412085385, 526, 2951391], 'label': '3456.oc.108.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936404
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bt1', '36.by1', '54.b1', '54.c1', '54.i1'], 'contains': ['216.cj1', '216.cm1', '216.dc1', '216.dg1', '216.di1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 13412085385, 526], 'label': '3456.oc.108.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936405
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bu1', '36.bx1', '54.a1', '54.d1', '54.i1'], 'contains': ['216.ck1', '216.cn1', '216.dc1', '216.dg1', '216.dk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 526, 2588323], 'label': '3456.oc.108.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936406
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.bv1', '36.bz1', '54.b1', '54.d1', '54.h1'], 'contains': ['216.cl1', '216.cn1', '216.dc1', '216.dh1', '216.dj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 13412085385, 526, 1968991665, 2588323], 'label': '3456.oc.108.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936407
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.ca1', '54.g1', '54.h1', '54.i1'], 'contains': ['216.bd1', '216.bf1', '216.bz1', '216.ca1', '216.cb1', '216.co1', '216.co2', '216.cp1', '216.cp2', '216.dc1', '216.dd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085385, 526, 1862886, 2588323, 1967535360], 'label': '3456.oc.108.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936408
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cb1', '36.cc1', '54.e1', '54.h1', '54.j1'], 'contains': ['216.bj1', '216.bl1', '216.cq1', '216.cr1', '216.cu1', '216.cw1', '216.cx1', '216.cz1', '216.dd1', '216.de1', '216.dh1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1968627499, 526, 2951391], 'label': '3456.oc.108.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936409
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cd1', '54.e1', '54.i1', '54.k1'], 'contains': ['216.bk1', '216.bm1', '216.cs1', '216.ct1', '216.cv1', '216.cy1', '216.cy2', '216.dd1', '216.dg1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1968627499, 526, 13415398178], 'label': '3456.oc.108.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936410
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.ce1', '36.cg1', '54.f1', '54.i1', '54.j1'], 'contains': ['216.cu1', '216.da1', '216.dd1', '216.di1', '216.dk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 2951738, 1968627499, 526], 'label': '3456.oc.108.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936411
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '32.46', 'aut_weyl_index': 1296, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cf1', '54.f1', '54.h1', '54.k1'], 'contains': ['216.cv1', '216.db1', '216.dd1', '216.dj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1968627499, 526, 13415397945], 'label': '3456.oc.108.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936412
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8666', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.m1', '6.n1', '6.o1'], 'contains': ['24.cv1', '24.cw1', '24.cx2', '24.dg1', '24.dh1', '36.bn1'], 'core': '192.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085646, 604203487, 38482338042, 2588202, 2951738, 1863007, 1967535360], 'label': '3456.oc.12.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936413
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.ch1', '36.ci1', '54.a1', '54.j1'], 'contains': ['216.cx1', '216.da1', '216.de1', '216.df1', '216.dk1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 526, 2951391], 'label': '3456.oc.108.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936414
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.cj1', '36.ck1', '54.a1', '54.b1', '54.k1'], 'contains': ['216.cy1', '216.db1', '216.df1', '216.dg1', '216.dj1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 526, 13415398178], 'label': '3456.oc.108.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936415
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cl1', '36.cm1', '54.b1', '54.j1'], 'contains': ['216.cz1', '216.da1', '216.df1', '216.dh1', '216.di1'], 'core': '864.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [1863259, 2587950, 1967536007, 2951738, 526], 'label': '3456.oc.108.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936416
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '36.co1', '36.cp1', '54.g1', '54.j1', '54.k1'], 'contains': ['216.a1', '216.ce1', '216.cf1', '216.dd1', '216.df1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1967536007, 526, 647, 1862886, 2588323], 'label': '3456.oc.108.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936417
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '24.bk1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.cq1', '36.cr1', '54.c1', '54.j1'], 'contains': ['216.a1', '216.de1', '216.di1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.108.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936418
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.cs1', '36.ct1', '36.cu1', '36.cv1', '54.c1', '54.d1', '54.k1'], 'contains': ['216.a1', '216.dg1', '216.dj1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [526, 647, 1862886, 2588323, 13415398178], 'label': '3456.oc.108.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936419
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1', '36.cx1', '36.cy1', '36.cz1', '36.da1', '54.d1', '54.j1'], 'contains': ['216.a1', '216.dh1', '216.dk1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.108.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936420
{'ambient': '3456.oc', 'aut_centralizer_order': 162, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '128.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1', '32.e1', '64.a1', '64.b1', '64.c1', '64.d1', '64.e1'], 'contains': ['384.a1', '384.b1', '384.c1', '384.d1', '384.e1'], 'core': '384.a1', 'coset_action_label': None, 'count': 16, 'diagramx': None, 'generators': [602743680, 1137421, 38480520960], 'label': '3456.oc.128.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '128.a1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936421
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '36.a1', 'complements': ['24.cz1', '24.da1', '24.u1', '24.v1', '24.w1', '24.db1'], 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '48.n1', '48.o1', '72.bq1', '72.bs1', '72.bw1', '72.bx1', '72.cd1'], 'contains': ['288.a1', '288.l1', '288.x1', '432.j1'], 'core': '144.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39799592563, 2588323, 1863007, 13413948127], 'label': '3456.oc.144.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1', 'normal_contained_in': ['36.a1', '48.a1'], 'normal_contains': ['288.a1', '576.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '3456.oc', 'quotient_action_image': '12.4', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936422
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.e1', '72.c1', '72.d1', '72.e1', '72.f1', '72.o1', '72.z1', '72.bz1'], 'contains': ['288.b1', '288.c1', '288.s1', '288.bc1', '288.cb1', '432.a1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 38481612978], 'label': '3456.oc.144.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936423
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.n1'], 'contains': ['24.cq1', '24.cw1', '24.cy1', '24.dj1', '24.dn1', '36.bo1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 13412085385, 2226652, 1863007], 'label': '3456.oc.12.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936424
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.f1', '72.c1', '72.g1', '72.i1', '72.j1', '72.p1', '72.q1', '72.ca1'], 'contains': ['288.b1', '288.e1', '288.ba1', '288.bi1', '288.cu1', '432.b1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 38480884533, 13412085120], 'label': '3456.oc.144.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936425
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '72.g1', '72.h1', '72.m1', '72.y1', '72.y2', '72.bz1'], 'contains': ['288.b1', '288.g1', '288.bd1', '288.bk1', '288.cw1', '432.c1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 1134693, 38480884533, 13412085120], 'label': '3456.oc.144.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936426
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.h1', '72.d1', '72.h1', '72.j1', '72.k1', '72.s1', '72.v1', '72.ca1'], 'contains': ['288.b1', '288.h1', '288.bj1', '288.bm1', '288.cx1', '432.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 13413948379, 1970078819, 38481613099], 'label': '3456.oc.144.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936427
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.i1', '72.c1', '72.h1', '72.k1', '72.l1', '72.p1', '72.w1', '72.cb1'], 'contains': ['288.b1', '288.bo1', '288.bp1', '432.e1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 38480884533, 13412085120], 'label': '3456.oc.144.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936428
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j1', '72.d1', '72.g1', '72.i1', '72.l1', '72.s1', '72.x1', '72.cb1'], 'contains': ['288.b1', '288.bq1', '288.br1', '432.f1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 13413948379, 38481613099], 'label': '3456.oc.144.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936429
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.k1', '72.e1', '72.m1', '72.n1', '72.y1', '72.y2', '72.cc1'], 'contains': ['288.b1', '288.d1', '288.g1', '288.w1', '288.be1', '288.cv1', '288.de1', '432.g1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 38480884533, 13412085120], 'label': '3456.oc.144.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936430
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l1', '72.f1', '72.i1', '72.k1', '72.n1', '72.y2', '72.cd1'], 'contains': ['288.b1', '288.d1', '288.x1', '288.bg1', '288.dd1', '432.h1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 1968627378, 38480884533, 13412085120], 'label': '3456.oc.144.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936431
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.i2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l2', '72.f1', '72.j1', '72.l1', '72.n1', '72.y1', '72.cd2'], 'contains': ['288.b1', '288.d1', '288.x2', '288.bg2', '288.dd2', '432.h2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627247, 1134693, 38480884533, 13412085120], 'label': '3456.oc.144.i2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.i2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936432
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.m1', '72.m1', '72.n1', '72.o1', '72.z1', '72.cc1'], 'contains': ['288.b1', '288.c1', '288.u1', '288.bu1', '288.cc1', '432.i1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 2588323, 38480884533, 13412085120], 'label': '3456.oc.144.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936433
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.a1', '48.c1', '72.p1', '72.s1', '72.y1', '72.z1', '72.cd1'], 'contains': ['288.a1', '288.b1', '288.v1', '432.j1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884412, 2588323, 1863007, 13413948127], 'label': '3456.oc.144.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936434
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 144, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.e1', '6.f1', '6.o1'], 'contains': ['24.cs1', '24.ct1', '24.cv1', '24.cw1', '24.cy1', '24.dk2', '24.dm1', '36.bp1', '36.bq1'], 'core': '384.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 13412085385, 2226275, 1863007], 'label': '3456.oc.12.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936435
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.k2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '18.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.p1', '72.q1', '72.v1', '72.w1', '72.x1', '72.y2', '72.z1', '72.cd2'], 'contains': ['288.b1', '288.v2', '288.bw1', '432.j2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 13413948258, 1863138, 2588323], 'label': '3456.oc.144.k2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.k2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936436
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.o1', '48.c1', '48.n1', '72.r1', '72.t1', '72.bb1'], 'contains': ['288.by1', '432.j1', '576.c1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137421, 2588323, 1863007, 13413948127], 'label': '3456.oc.144.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '144.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936437
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.p1', '48.c1', '48.o1', '72.u1'], 'contains': ['288.bz1', '432.j1', '576.d1'], 'core': '864.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [38482336681, 2588323, 1863007, 13413948127], 'label': '3456.oc.144.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1', 'old_label': '144.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936438
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.q1', '72.e1', '72.m1', '72.n1', '72.ba1', '72.bz1'], 'contains': ['288.c1', '288.d1', '288.g1', '288.cd1', '288.cj1', '288.da1', '288.dn1', '432.k1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 38481612726, 1862886, 13412085120], 'label': '3456.oc.144.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936439
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.r1', '72.e1', '72.f1', '72.n1', '72.ba1', '72.cc1'], 'contains': ['288.c1', '288.d1', '288.ce1', '288.cl1', '288.cz1', '432.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352442, 13412085120], 'label': '3456.oc.144.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936440
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '72.e1', '72.m1', '72.ce1'], 'contains': ['288.c1', '288.g1', '288.ci1', '288.cn1', '288.do1', '432.m1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352190, 13412085120], 'label': '3456.oc.144.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936441
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.d1', '48.v1', '72.o1', '72.ba1', '72.ce1'], 'contains': ['288.c1', '288.ch1', '288.cp1', '432.n1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 38480883894, 13414673070, 1862886], 'label': '3456.oc.144.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
-
id: 201936442
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.o1', '48.d1', '48.t1', '72.bc1'], 'contains': ['288.cr1', '432.n1', '576.c1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 48, 'diagramx': None, 'generators': [1137421, 2587950, 13414673070, 1862886], 'label': '3456.oc.144.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.bf1', 'old_label': '144.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201936443
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.p1', '48.d1', '48.u1'], 'contains': ['288.cs1', '432.n1', '576.d1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [2587950, 38482336681, 13414673070, 1862886], 'label': '3456.oc.144.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1', 'old_label': '144.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201936444
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.w1', '72.j1', '72.ca1'], 'contains': ['288.d1', '288.e1', '288.h1', '288.cy1', '288.db1', '288.dl1', '288.dp1', '432.o1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 38480520960, 2226652, 13412085120], 'label': '3456.oc.144.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '144.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936445
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8418', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.n1'], 'contains': ['24.cu1', '24.cv1', '24.cy1', '24.dl1', '24.dn1', '36.br1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [604203487, 38482338042, 2588202, 1967536007, 2951738, 13412085385, 1863007], 'label': '3456.oc.12.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936446
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '48.x1'], 'contains': ['288.f1', '288.i1', '288.k1', '288.df1', '288.dg1', '432.r1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [1967901282, 1137042, 2226652, 13412085120], 'label': '3456.oc.144.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.u1', 'old_label': '144.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936447
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.e1', '72.bd1', '72.be1', '72.bf1', '72.bg1', '72.bp1', '72.bx1', '72.bz1'], 'contains': ['288.l1', '288.m1', '288.s1', '288.bd1', '288.cd1', '432.a1'], 'core': '576.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13412085646, 39797775360, 526, 1862886], 'label': '3456.oc.144.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936448
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.f1', '72.bd1', '72.bh1', '72.bj1', '72.bk1', '72.bq1', '72.br1', '72.ca1'], 'contains': ['288.l1', '288.o1', '288.ba1', '288.bj1', '288.cy1', '432.b1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2226652, 39798138933, 13412085120], 'label': '3456.oc.144.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936449
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.g1', '72.bh1', '72.bi1', '72.bn1', '72.bw1', '72.bw2', '72.bz1'], 'contains': ['288.l1', '288.p1', '288.bc1', '288.bk1', '288.da1', '432.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693, 38480884533], 'label': '3456.oc.144.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936450
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.h1', '72.be1', '72.bi1', '72.bk1', '72.bl1', '72.bs1', '72.bt1', '72.ca1'], 'contains': ['288.l1', '288.q1', '288.bi1', '288.bm1', '288.db1', '432.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 13413948379, 1970078819, 39798867499], 'label': '3456.oc.144.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936451
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.bu1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.i1', '72.bd1', '72.bi1', '72.bl1', '72.bm1', '72.bq1', '72.bu1', '72.cb1'], 'contains': ['288.l1', '288.bo1', '288.bq1', '432.e1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2951738, 39798138933, 13412085120], 'label': '3456.oc.144.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936452
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.j1', '72.be1', '72.bh1', '72.bj1', '72.bm1', '72.bs1', '72.bv1', '72.cb1'], 'contains': ['288.l1', '288.bp1', '288.br1', '432.f1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 13413948379, 39798867499], 'label': '3456.oc.144.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936453
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.k1', '72.bf1', '72.bn1', '72.bo1', '72.bw1', '72.bw2', '72.cc1'], 'contains': ['288.l1', '288.n1', '288.p1', '288.u1', '288.be1', '288.cz1', '288.de1', '432.g1'], 'core': '576.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 13413948379, 38480884533], 'label': '3456.oc.144.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936454
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l1', '72.bg1', '72.bj1', '72.bl1', '72.bo1', '72.bw2', '72.cd1'], 'contains': ['288.l1', '288.n1', '288.v1', '288.bg1', '288.dd1', '432.h1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1134693, 1968627378, 38480884533], 'label': '3456.oc.144.bc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.bc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936455
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.bc2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.l2', '72.bg1', '72.bk1', '72.bm1', '72.bo1', '72.bw1', '72.cd2'], 'contains': ['288.l1', '288.n1', '288.v2', '288.bg2', '288.dd2', '432.h2'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1968627247, 1134693, 13413948127, 38480884533], 'label': '3456.oc.144.bc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.bc2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936456
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.g1', '6.n1'], 'contains': ['24.cq1', '24.cv1', '24.do1', '24.dq1', '24.dv1', '36.bs1', '36.bw1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 13412085385, 526, 602744206, 2951391], 'label': '3456.oc.12.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201936457
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.m1', '72.bn1', '72.bo1', '72.bp1', '72.bx1', '72.cc1'], 'contains': ['288.l1', '288.m1', '288.w1', '288.bu1', '288.ce1', '432.i1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39799592563, 1862886, 2588323, 13412085120], 'label': '3456.oc.144.bd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.bd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936458
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '18.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.p1', '72.br1', '72.bt1', '72.bu1', '72.bv1', '72.bw2', '72.bx1', '72.cd2'], 'contains': ['288.l1', '288.x2', '288.bw1', '432.j2'], 'core': '576.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [39799592563, 13413948258, 1863138, 2588323], 'label': '3456.oc.144.be1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.be1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936459
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.q1', '72.bf1', '72.bn1', '72.bo1', '72.by1', '72.bz1'], 'contains': ['288.m1', '288.n1', '288.p1', '288.cb1', '288.cj1', '288.cw1', '288.dn1', '432.k1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1967536007, 38481612726, 1862886], 'label': '3456.oc.144.bf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936460
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.r1', '72.bf1', '72.bg1', '72.bo1', '72.by1', '72.cc1'], 'contains': ['288.m1', '288.n1', '288.cc1', '288.cl1', '288.cv1', '432.l1'], 'core': '576.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 1969352442, 13414673322], 'label': '3456.oc.144.bg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936461
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.s1', '72.bf1', '72.bn1', '72.ce1'], 'contains': ['288.m1', '288.p1', '288.ch1', '288.cn1', '288.do1', '432.m1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 1969352190], 'label': '3456.oc.144.bh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936462
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.t1', '48.u1', '48.v1', '72.bp1', '72.by1', '72.ce1'], 'contains': ['288.m1', '288.ci1', '288.cp1', '432.n1'], 'core': '576.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [2587950, 39799592190, 13414673070, 1862886], 'label': '3456.oc.144.bi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '144.bi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
-
id: 201936463
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.w1', '72.bk1', '72.ca1'], 'contains': ['288.n1', '288.o1', '288.q1', '288.cu1', '288.cx1', '288.dl1', '288.dp1', '432.o1'], 'core': '576.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 38480520960, 2226652, 13413948127], 'label': '3456.oc.144.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '144.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936464
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.y1', '72.bz1', '72.ca1', '72.cb1', '72.cc1', '72.cd1', '72.cd2'], 'contains': ['288.b1', '288.d1', '288.l1', '288.n1', '288.r1', '288.y1', '288.dc1', '432.p1'], 'core': '576.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 1967535360, 38480884533, 13412085120], 'label': '3456.oc.144.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936465
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.z1', '72.bz1', '72.cc1', '72.ce1'], 'contains': ['288.c1', '288.g1', '288.m1', '288.p1', '288.r1', '288.cf1', '288.dj1', '432.q1'], 'core': '576.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 1862886, 1967535360, 13412085120], 'label': '3456.oc.144.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936466
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.x1', '48.ba1', '72.ca1'], 'contains': ['288.e1', '288.h1', '288.o1', '288.q1', '288.r1', '288.dh1', '288.dk1', '432.r1'], 'core': '576.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [38480520960, 2226652, 1967535360, 13412085120], 'label': '3456.oc.144.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '144.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936467
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 216, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.g1', '6.o1'], 'contains': ['24.cs1', '24.cv1', '24.do1', '24.ds1', '24.du1', '36.bt1', '36.by1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 13412085385, 526, 602744206], 'label': '3456.oc.12.bj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201936468
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bb1', '72.o1', '72.bf1', '72.ch1', '72.ci1', '72.cm1', '72.dr1', '72.fm1'], 'contains': ['288.s1', '288.u1', '288.cb1', '288.cc1', '288.ch1', '432.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085385, 526, 1862886, 38481612978], 'label': '3456.oc.144.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936469
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bc1', '72.z1', '72.bg1', '72.cf1', '72.cg1', '72.cj1', '72.cn1', '72.dr1'], 'contains': ['288.s1', '288.v1', '288.v2', '288.cc1', '432.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [526, 1862886, 13414673191, 38481612978], 'label': '3456.oc.144.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936470
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bb1', '72.e1', '72.bp1', '72.ch1', '72.ci1', '72.cj1', '72.ds1', '72.fn1'], 'contains': ['288.s1', '288.w1', '288.cd1', '288.ce1', '288.ci1', '432.s1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085385, 39797775360, 526, 1862886], 'label': '3456.oc.144.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936471
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bc1', '72.f1', '72.bx1', '72.ck1', '72.cl1', '72.cm1', '72.cn1', '72.ds1'], 'contains': ['288.s1', '288.x1', '288.x2', '288.ce1', '432.t1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39797775360, 526, 1862886, 13414673191], 'label': '3456.oc.144.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936472
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bd1', '72.bz1', '72.ch1', '72.cn1', '72.co1', '72.cq1', '72.dt1', '72.fo1'], 'contains': ['288.s1', '288.y1', '288.bk1', '288.cf1', '288.cj1', '432.u1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [526, 1862886, 38481612978, 1967535360], 'label': '3456.oc.144.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936473
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.bd1', '72.cp1', '72.du1', '72.fp1'], 'contains': ['288.t1', '288.z1', '288.bl1', '288.cg1', '288.ck1', '432.u1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [37882941618, 526, 1862886, 1967535360], 'label': '3456.oc.144.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936474
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.be1', '72.c1', '72.bd1', '72.cf1', '72.ck1', '72.co1', '72.cr1', '72.fq1'], 'contains': ['288.s1', '288.ba1', '288.bo1', '432.v1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [265, 38481612847, 1862886, 2226652], 'label': '3456.oc.144.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936475
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.be1', '72.cp1', '72.cs1', '72.fr1'], 'contains': ['288.t1', '288.bb1', '288.bs1', '432.v1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882941487, 265, 1862886, 2226652], 'label': '3456.oc.144.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936476
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bf1', '72.e1', '72.bf1', '72.cj1', '72.cm1', '72.dt1', '72.dv1', '72.fs1'], 'contains': ['288.s1', '288.be1', '288.cj1', '288.cl1', '288.cn1', '432.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 526, 1862886, 38481612978], 'label': '3456.oc.144.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936477
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.bf1', '72.du1', '72.dw1', '72.ft1'], 'contains': ['288.t1', '288.bf1', '288.ck1', '288.cm1', '288.co1', '432.w1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 37882941618, 526, 1862886], 'label': '3456.oc.144.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '144.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936478
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3456.hx', 'aut_weyl_index': 12, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.e1', '6.f1', '6.g1', '6.j1', '6.l1', '6.m1', '6.n1', '6.o1', '6.s1', '6.t1', '9.b1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [13412085385, 1862886, 2951738, 647, 1967536007, 2588323, 526, 38480884412, 604203618], 'label': '3456.oc.3.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936479
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.j1', '6.o1'], 'contains': ['24.ct1', '24.cw1', '24.do1', '24.ds1', '24.dw1', '36.bu1', '36.bx1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 1968991316, 13412085385, 38480884412, 526, 2588323, 602744206], 'label': '3456.oc.12.bk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936480
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bg1', '72.f1', '72.bg1', '72.ci1', '72.cr1', '72.ct1', '72.dv1', '72.fo1'], 'contains': ['288.s1', '288.bg1', '288.bg2', '288.cl1', '432.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1969352563, 526, 1862886, 38481612978], 'label': '3456.oc.144.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936481
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.bg1', '72.cs1', '72.dw1', '72.fp1'], 'contains': ['288.t1', '288.bh1', '288.bh2', '288.cm1', '432.x1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1969352563, 37882941618, 526, 1862886], 'label': '3456.oc.144.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936482
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bh1', '72.c1', '72.be1', '72.cf1', '72.cl1', '72.cq1', '72.ct1', '72.fu1'], 'contains': ['288.s1', '288.bi1', '288.bp1', '432.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 38481612847, 13413586612, 1862886], 'label': '3456.oc.144.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936483
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bh1', '72.d1', '72.bd1', '72.cg1', '72.ck1', '72.cq1', '72.ct1', '72.fv1'], 'contains': ['288.s1', '288.bj1', '288.bq1', '432.y1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [265, 39797775360, 13413586612, 1862886], 'label': '3456.oc.144.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936484
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bi1', '72.d1', '72.be1', '72.cg1', '72.cl1', '72.co1', '72.cr1', '72.fw1'], 'contains': ['288.s1', '288.bm1', '288.br1', '432.z1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 526, 1968991665, 1134054], 'label': '3456.oc.144.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936485
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.bi1', '72.cp1', '72.cs1', '72.fx1'], 'contains': ['288.t1', '288.bn1', '288.bt1', '432.z1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882213052, 526, 1968991665, 1134054], 'label': '3456.oc.144.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936486
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bj1', '72.m1', '72.bf1', '72.dm1', '72.dn1', '72.eo1', '72.eo2'], 'contains': ['288.u1', '288.bd1', '288.be1', '288.cv1', '288.cw1', '288.dn1', '288.do1', '432.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 13413948006, 38480884533], 'label': '3456.oc.144.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936487
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.ce1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bl1', '72.q1', '72.bk1', '72.cf1', '72.cu1', '72.dc1', '72.dg1', '72.dx1'], 'contains': ['288.v2', '288.ba1', '288.bi1', '288.cu1', '432.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 13413948127, 38480884533], 'label': '3456.oc.144.ce1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ce1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ce1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936488
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.cf1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bm1', '72.p1', '72.bj1', '72.cf1', '72.cv1', '72.dd1', '72.dh1', '72.dy1'], 'contains': ['288.v1', '288.ba1', '288.bp1', '432.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 38480884533], 'label': '3456.oc.144.cf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cf1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936489
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bn1', '72.y1', '72.bg1', '72.cv1', '72.cx1', '72.dn1', '72.en2'], 'contains': ['288.v1', '288.bd1', '288.bg2', '288.cv1', '432.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1968627247, 1134693, 38480884533], 'label': '3456.oc.144.cg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.cg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936490
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.f1', '6.j1', '6.n1'], 'contains': ['24.cu1', '24.cw1', '24.do1', '24.dt1', '24.dv1', '36.bv1', '36.bz1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 13412085385, 38480884412, 526, 1968991665, 2588323, 602744206], 'label': '3456.oc.12.bl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936491
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cg2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bn2', '72.y2', '72.bg1', '72.cu1', '72.cw1', '72.dn1', '72.en1'], 'contains': ['288.v2', '288.bd1', '288.bg1', '288.cv1', '432.be2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 13413948127, 1968627378, 38480884533], 'label': '3456.oc.144.cg2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.cg2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cg2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936492
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.ch1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bq1', '72.p1', '72.bl1', '72.cf1', '72.cx1', '72.de1', '72.di1', '72.dz1'], 'contains': ['288.v1', '288.bi1', '288.bo1', '432.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 38480884533], 'label': '3456.oc.144.ch1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ch1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ch1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936493
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ci1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bp1', '72.v1', '72.bk1', '72.cg1', '72.cw1', '72.dc1', '72.dj1', '72.ea1'], 'contains': ['288.v2', '288.bj1', '288.bm1', '288.cx1', '432.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078819, 13413219692, 38481613099], 'label': '3456.oc.144.ci1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ci1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ci1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936494
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.br1', '72.s1', '72.bj1', '72.cg1', '72.cx1', '72.de1', '72.dh1', '72.eb1'], 'contains': ['288.v1', '288.bj1', '288.br1', '432.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 13414673322, 38481613099], 'label': '3456.oc.144.cj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cj1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936495
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ck1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bs1', '72.s1', '72.bl1', '72.cg1', '72.cv1', '72.dd1', '72.di1', '72.ec1'], 'contains': ['288.v1', '288.bm1', '288.bq1', '432.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078819, 13414673322, 38481613099], 'label': '3456.oc.144.ck1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ck1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ck1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936496
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.cl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bt1', '72.w1', '72.bm1', '72.cf1', '72.cw1', '72.df1', '72.dj1', '72.dx1'], 'contains': ['288.v2', '288.bo1', '288.bp1', '432.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 13413948127, 38480884533], 'label': '3456.oc.144.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cl1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936497
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cm1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bu1', '72.x1', '72.bm1', '72.cg1', '72.cu1', '72.df1', '72.dg1', '72.ea1'], 'contains': ['288.v2', '288.bq1', '288.br1', '432.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 13413219692, 38481613099], 'label': '3456.oc.144.cm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cm1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936498
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cn1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bj1', '72.e1', '72.bn1', '72.dm1', '72.do1', '72.eo1', '72.eo2'], 'contains': ['288.w1', '288.bc1', '288.be1', '288.cz1', '288.da1', '288.dn1', '288.do1', '432.ba1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085767, 1134693, 1968627499, 38480884533], 'label': '3456.oc.144.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936499
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.co1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bk1', '72.cc1', '72.ch1', '72.dm1', '72.dp1', '72.en1', '72.en2'], 'contains': ['288.u1', '288.w1', '288.y1', '288.cv1', '288.cz1', '288.dc1', '288.dj1', '432.bb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1134693, 1967535360, 38480884533], 'label': '3456.oc.144.co1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.co1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.co1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936500
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cp1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bn3', '72.n1', '72.bo1', '72.ci1', '72.dn1', '72.do1', '72.en1', '72.eo1'], 'contains': ['288.u1', '288.w1', '288.bg1', '288.cv1', '288.cz1', '288.dd2', '288.dn1', '432.be3'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1134693, 1968627378, 38480884533], 'label': '3456.oc.144.cp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936501
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1031', 'aut_weyl_index': 144, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.n1', '6.o1'], 'contains': ['24.bm1', '24.bo1', '24.ci1', '24.cj1', '24.ck1', '24.cx1', '24.cx2', '24.cy1', '24.cy2', '24.do1', '24.dp1', '36.ca1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [38480884129, 13412085385, 526, 1862886, 2588323, 604203618, 1967535360], 'label': '3456.oc.12.bm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
-
id: 201936502
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cp2', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bn4', '72.n1', '72.bo1', '72.ci1', '72.dn1', '72.do1', '72.en2', '72.eo2'], 'contains': ['288.u1', '288.w1', '288.bg2', '288.cv1', '288.cz1', '288.dd1', '288.dn1', '432.be4'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1968627247, 1134693, 13412085385, 38480884533], 'label': '3456.oc.144.cp2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cp2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cp2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936503
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cq1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bo1', '72.m1', '72.bn1', '72.ch1', '72.dq1', '72.eo1', '72.eo2'], 'contains': ['288.u1', '288.w1', '288.bk1', '288.cw1', '288.da1', '288.de1', '288.do1', '432.bf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967536007, 1134693, 13412085385, 38480884533], 'label': '3456.oc.144.cq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936504
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cr1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bv1', '72.y1', '72.bo1', '72.cj1', '72.dn1', '72.dp1', '72.dq1', '72.eo1'], 'contains': ['288.v1', '288.w1', '288.be1', '288.cv1', '288.cw1', '288.dd2', '288.de1', '432.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13413948258, 1134693, 1968627499, 38480884533], 'label': '3456.oc.144.cr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936505
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cr2', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bv2', '72.y2', '72.bo1', '72.cj1', '72.dn1', '72.dp1', '72.dq1', '72.eo2'], 'contains': ['288.v2', '288.w1', '288.be1', '288.cv1', '288.cw1', '288.dd1', '288.de1', '432.bm2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 1968627499, 13413948127, 38480884533], 'label': '3456.oc.144.cr2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.cr2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cr2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936506
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.cs1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bl1', '72.j1', '72.br1', '72.ck1', '72.cy1', '72.dc1', '72.dh1', '72.ef1'], 'contains': ['288.x2', '288.ba1', '288.bj1', '288.cy1', '432.bc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2226652, 39798138933, 13413948127], 'label': '3456.oc.144.cs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.cs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cs1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936507
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.ct1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bm1', '72.i1', '72.bq1', '72.ck1', '72.cz1', '72.dd1', '72.dg1', '72.eg1'], 'contains': ['288.x1', '288.ba1', '288.bq1', '432.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 39798138933], 'label': '3456.oc.144.ct1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.ct1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ct1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936508
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cu1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bn1', '72.f1', '72.bw1', '72.cz1', '72.db1', '72.do1', '72.en2'], 'contains': ['288.x1', '288.bc1', '288.bg2', '288.cz1', '432.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1968627247, 1134693, 38480884533], 'label': '3456.oc.144.cu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.cu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936509
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.cu2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bn2', '72.f1', '72.bw2', '72.cy1', '72.da1', '72.do1', '72.en1'], 'contains': ['288.x2', '288.bc1', '288.bg1', '288.cz1', '432.be2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1134693, 1968627378, 38480884533], 'label': '3456.oc.144.cu2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.cu2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cu2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936510
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bp1', '72.j1', '72.bt1', '72.cl1', '72.da1', '72.dc1', '72.di1', '72.eh1'], 'contains': ['288.x2', '288.bi1', '288.bm1', '288.db1', '432.bg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078819, 13413219692, 39798867499], 'label': '3456.oc.144.cv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cv1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936511
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.br1', '72.i1', '72.bs1', '72.cl1', '72.db1', '72.de1', '72.dg1', '72.ei1'], 'contains': ['288.x1', '288.bi1', '288.br1', '432.bi1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 39798867499, 13414673322], 'label': '3456.oc.144.cw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936512
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1', '6.n1', '6.s1'], 'contains': ['24.bs1', '24.bu1', '24.dc1', '24.dd1', '24.dg1', '24.di1', '24.dj1', '24.dl1', '24.dp1', '24.dq1', '24.dt1', '36.cb1', '36.cc1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 602744206, 2951391], 'label': '3456.oc.12.bn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936513
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.cx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bq1', '72.k1', '72.bq1', '72.ck1', '72.db1', '72.de1', '72.dj1', '72.ej1'], 'contains': ['288.x1', '288.bj1', '288.bo1', '432.bh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 39798138933], 'label': '3456.oc.144.cx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.cx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936514
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.cy1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bs1', '72.k1', '72.bs1', '72.cl1', '72.cz1', '72.dd1', '72.dj1', '72.ek1'], 'contains': ['288.x1', '288.bm1', '288.bp1', '432.bj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078819, 39798867499, 13414673322], 'label': '3456.oc.144.cy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.cy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936515
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.cz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '72.bu1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bt1', '72.l1', '72.bu1', '72.ck1', '72.da1', '72.df1', '72.di1', '72.ef1'], 'contains': ['288.x2', '288.bo1', '288.bq1', '432.bk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1134693, 2951738, 39798138933, 13413948127], 'label': '3456.oc.144.cz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.cz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cz1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936516
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.da1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bu1', '72.l1', '72.bv1', '72.cl1', '72.cy1', '72.df1', '72.dh1', '72.eh1'], 'contains': ['288.x2', '288.bp1', '288.br1', '432.bl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1863259, 1970078440, 13413219692, 39798867499], 'label': '3456.oc.144.da1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.da1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.da1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936517
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.db1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bv1', '72.n1', '72.bw1', '72.cm1', '72.do1', '72.dp1', '72.dq1', '72.eo1'], 'contains': ['288.u1', '288.x1', '288.be1', '288.cz1', '288.da1', '288.dd2', '288.de1', '432.bm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1134693, 13412085385, 1968627499, 38480884533], 'label': '3456.oc.144.db1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.db1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936518
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.db2', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.bv2', '72.n1', '72.bw2', '72.cm1', '72.do1', '72.dp1', '72.dq1', '72.eo2'], 'contains': ['288.u1', '288.x2', '288.be1', '288.cz1', '288.da1', '288.dd1', '288.de1', '432.bm2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085646, 1134693, 1968627499, 38480884533], 'label': '3456.oc.144.db2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.db2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.db2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936519
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.dc1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw1', '72.cd1', '72.cn1', '72.dd1', '72.de1', '72.dp1', '72.en2'], 'contains': ['288.v1', '288.x1', '288.y1', '288.dc1', '288.dd1', '432.bn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1134693, 1967535360, 38480884533], 'label': '3456.oc.144.dc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.dc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936520
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.dc2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bw2', '72.cd2', '72.cn1', '72.dc1', '72.df1', '72.dp1', '72.en1'], 'contains': ['288.v2', '288.x2', '288.y1', '288.dc1', '288.dd2', '432.bn2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1134693, 13413948127, 1967535360, 38480884533], 'label': '3456.oc.144.dc2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.dc2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dc2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936521
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.dd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bx1', '72.y1', '72.bw2', '72.cn1', '72.dh1', '72.di1', '72.dq1'], 'contains': ['288.v1', '288.x2', '288.bk1', '288.de1', '432.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13413948258, 1967536007, 1134693, 38480884533], 'label': '3456.oc.144.dd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.dd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936522
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.dd2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bx1', '72.y2', '72.bw1', '72.cn1', '72.dg1', '72.dj1', '72.dq1'], 'contains': ['288.v2', '288.x1', '288.bk1', '288.de1', '432.bo1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 1134693, 13413948127, 38480884533], 'label': '3456.oc.144.dd2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.dd2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dd2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936523
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.l1', '6.o1', '6.t1'], 'contains': ['24.bt1', '24.bv1', '24.de1', '24.df1', '24.dh1', '24.dk1', '24.dk2', '24.dp1', '24.ds1', '36.cd1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 13415398178, 602744206], 'label': '3456.oc.12.bo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936524
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.de1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.by1', '72.ca1', '72.co1', '72.dc1', '72.dd1', '72.dk1', '72.er1', '72.et1'], 'contains': ['288.y1', '288.ba1', '288.bm1', '288.dh1', '288.dl1', '432.bp1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 1967535360, 38480884533], 'label': '3456.oc.144.de1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.de1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.de1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936525
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.df1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.by1', '72.cp1', '72.es1', '72.eu1'], 'contains': ['288.z1', '288.bb1', '288.bn1', '288.di1', '288.dm1', '432.bp1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 37882213173, 2226652, 1967535360], 'label': '3456.oc.144.df1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.df1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.df1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936526
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.dg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.bz1', '72.bz1', '72.dk1', '72.dl1', '72.dm1', '72.en1', '72.en2'], 'contains': ['288.y1', '288.bc1', '288.bd1', '288.dj1', '288.dn1', '432.bq1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085767, 1134693, 1967535360, 38480884533], 'label': '3456.oc.144.dg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.dg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936527
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.dh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ca1', '72.ca1', '72.cq1', '72.dc1', '72.de1', '72.dl1', '72.ev1', '72.ew1'], 'contains': ['288.y1', '288.bi1', '288.bj1', '288.dk1', '288.dp1', '432.br1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 13414311772, 1967535360, 38480884533], 'label': '3456.oc.144.dh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936528
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.di1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cb1', '72.cb1', '72.co1', '72.de1', '72.df1', '72.dl1', '72.er1', '72.ex1'], 'contains': ['288.y1', '288.bo1', '288.br1', '432.bs1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 1967535360, 38480884533], 'label': '3456.oc.144.di1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.di1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.di1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936529
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.dj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cc1', '72.cb1', '72.cq1', '72.dd1', '72.df1', '72.dk1', '72.ev1', '72.ey1'], 'contains': ['288.y1', '288.bp1', '288.bq1', '432.bt1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13415036858, 1134693, 1967535360, 38480884533], 'label': '3456.oc.144.dj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936530
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.dk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cb1', '72.cp1', '72.es1', '72.ez1'], 'contains': ['288.z1', '288.bs1', '288.bt1', '432.bs1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 37882213173, 1967535360], 'label': '3456.oc.144.dk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.dk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936531
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.dl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cd1', '72.c1', '72.bh1', '72.cy1', '72.cz1', '72.dk1', '72.dx1', '72.dy1'], 'contains': ['288.ba1', '288.bc1', '288.bp1', '432.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 38480884533], 'label': '3456.oc.144.dl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dl1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936532
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.dm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cd1', '72.g1', '72.bd1', '72.cu1', '72.cv1', '72.dk1', '72.ef1', '72.eg1'], 'contains': ['288.ba1', '288.bd1', '288.bq1', '432.bu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1134693, 2226652, 39798138933], 'label': '3456.oc.144.dm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.dm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dm1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936533
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ce1', '72.j1', '72.bk1', '72.cr1', '72.cv1', '72.cz1', '72.et1', '72.fa1'], 'contains': ['288.ba1', '288.bg2', '288.bm1', '288.dl1', '432.bv1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2226652, 38480884533], 'label': '3456.oc.144.dn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dn1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936534
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.m1', '6.o1', '6.s1'], 'contains': ['24.dg1', '24.dm1', '24.dp1', '24.du1', '24.dw1', '36.ce1', '36.cg1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 2951738, 1968627499, 526, 602744206], 'label': '3456.oc.12.bp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936535
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.do1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.ce1', '72.cs1', '72.eu1', '72.fb1'], 'contains': ['288.bb1', '288.bh2', '288.bn1', '288.dm1', '432.bv1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 37882213173, 2226652], 'label': '3456.oc.144.do1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.do1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.do1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936536
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cf1', '72.i1', '72.bj1', '72.cr1', '72.cu1', '72.cy1', '72.er1', '72.fc1'], 'contains': ['288.ba1', '288.bg1', '288.br1', '432.bw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2226652, 1968627378, 38480884533], 'label': '3456.oc.144.dp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936537
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cf1', '72.cs1', '72.es1', '72.fd1'], 'contains': ['288.bb1', '288.bh1', '288.bt1', '432.bw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 37882213173, 2226652, 1968627378], 'label': '3456.oc.144.dq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.dq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936538
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dr1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cg1', '72.g1', '72.bh1', '72.co1', '72.dg1', '72.dh1', '72.fa1', '72.fc1'], 'contains': ['288.ba1', '288.bk1', '288.br1', '432.bx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2226652, 38480884533], 'label': '3456.oc.144.dr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dr1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936539
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ds1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cg1', '72.cp1', '72.fb1', '72.fd1'], 'contains': ['288.bb1', '288.bl1', '288.bt1', '432.bx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 37882213173, 2226652], 'label': '3456.oc.144.ds1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.ds1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ds1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936540
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.dt1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ch1', '72.c1', '72.bi1', '72.da1', '72.db1', '72.dl1', '72.dx1', '72.dz1'], 'contains': ['288.bc1', '288.bi1', '288.bo1', '432.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 38480884533], 'label': '3456.oc.144.dt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dt1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936541
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.du1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ci1', '72.d1', '72.bh1', '72.cy1', '72.db1', '72.dl1', '72.ea1', '72.eb1'], 'contains': ['288.bc1', '288.bj1', '288.br1', '432.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078440, 38481613099], 'label': '3456.oc.144.du1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.du1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.du1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936542
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dv1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cj1', '72.d1', '72.bi1', '72.cz1', '72.da1', '72.dk1', '72.ea1', '72.ec1'], 'contains': ['288.bc1', '288.bm1', '288.bq1', '432.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078819, 38481613099], 'label': '3456.oc.144.dv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936543
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dw1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ci1', '72.g1', '72.be1', '72.cu1', '72.cx1', '72.dl1', '72.eh1', '72.ei1'], 'contains': ['288.bd1', '288.bi1', '288.br1', '432.bz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078440, 39798867499], 'label': '3456.oc.144.dw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936544
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.dx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ch1', '72.h1', '72.bd1', '72.cw1', '72.cx1', '72.dl1', '72.ef1', '72.ej1'], 'contains': ['288.bd1', '288.bj1', '288.bo1', '432.by1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085767, 1134693, 2951738, 39798138933], 'label': '3456.oc.144.dx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.dx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dx1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936545
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.m1', '6.n1', '6.t1'], 'contains': ['24.dh1', '24.dn1', '24.dp1', '24.dv1', '36.cf1'], 'core': '48.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1968627499, 526, 602744206, 13415397945], 'label': '3456.oc.12.bq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936546
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dy1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cj1', '72.h1', '72.be1', '72.cv1', '72.cw1', '72.dk1', '72.eh1', '72.ek1'], 'contains': ['288.bd1', '288.bm1', '288.bp1', '432.ca1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1863259, 1970078819, 39798867499], 'label': '3456.oc.144.dy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936547
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.dz1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ck1', '72.i1', '72.bl1', '72.ct1', '72.cu1', '72.da1', '72.ev1', '72.fe1'], 'contains': ['288.bg1', '288.bi1', '288.bq1', '432.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 13414311772, 1968627378, 38480884533], 'label': '3456.oc.144.dz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.dz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.dz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936548
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ea1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ck1', '72.k1', '72.bj1', '72.ct1', '72.cw1', '72.cy1', '72.ev1', '72.fg1'], 'contains': ['288.bg1', '288.bj1', '288.bp1', '432.cb1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13415036858, 1134693, 1968627378, 38480884533], 'label': '3456.oc.144.ea1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ea1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ea1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936549
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.eb1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cl1', '72.j1', '72.bk1', '72.ct1', '72.cx1', '72.db1', '72.ew1', '72.ff1'], 'contains': ['288.bg2', '288.bi1', '288.bj1', '288.dp1', '432.cc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 13414311772, 38480884533], 'label': '3456.oc.144.eb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.eb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eb1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936550
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ec1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cm1', '72.k1', '72.bl1', '72.cr1', '72.cw1', '72.da1', '72.er1', '72.fh1'], 'contains': ['288.bg1', '288.bm1', '288.bo1', '432.cd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 1968627378, 38480884533], 'label': '3456.oc.144.ec1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ec1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ec1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936551
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ed1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cm1', '72.cs1', '72.es1', '72.fi1'], 'contains': ['288.bh1', '288.bn1', '288.bs1', '432.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1134693, 2951738, 37882213173, 1968627378], 'label': '3456.oc.144.ed1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.ed1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ed1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936552
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ee1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cn1', '72.l1', '72.bm1', '72.cr1', '72.cx1', '72.db1', '72.ex1', '72.fa1'], 'contains': ['288.bg2', '288.bo1', '288.br1', '432.ce1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738, 38480884533], 'label': '3456.oc.144.ee1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ee1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ee1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936553
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ef1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.co1', '72.l1', '72.bm1', '72.ct1', '72.cv1', '72.cz1', '72.ey1', '72.ff1'], 'contains': ['288.bg2', '288.bp1', '288.bq1', '432.cf1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 13415036858, 1134693, 38480884533], 'label': '3456.oc.144.ef1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ef1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ef1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936554
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.eg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cn1', '72.cs1', '72.ez1', '72.fb1'], 'contains': ['288.bh2', '288.bs1', '288.bt1', '432.ce1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738, 37882213173], 'label': '3456.oc.144.eg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.eg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936555
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.eh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cp1', '72.g1', '72.bi1', '72.cq1', '72.dg1', '72.di1', '72.fe1', '72.ff1'], 'contains': ['288.bi1', '288.bk1', '288.bq1', '432.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 13414311772, 38480884533], 'label': '3456.oc.144.eh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.eh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eh1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936556
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.e1', '6.s1'], 'contains': ['24.dj1', '24.dm1', '24.dq1', '24.dr1', '24.dw1', '36.ch1', '36.ci1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 602744206, 2951391], 'label': '3456.oc.12.br1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.br1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936557
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ei1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cp1', '72.h1', '72.bh1', '72.cq1', '72.dh1', '72.dj1', '72.ff1', '72.fg1'], 'contains': ['288.bj1', '288.bk1', '288.bp1', '432.cg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13415036858, 1967536007, 1134693, 38480884533], 'label': '3456.oc.144.ei1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ei1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ei1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936558
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ej1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cq1', '72.h1', '72.bi1', '72.co1', '72.di1', '72.dj1', '72.fa1', '72.fh1'], 'contains': ['288.bk1', '288.bm1', '288.bo1', '432.ch1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738, 38480884533], 'label': '3456.oc.144.ej1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.ej1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ej1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936559
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ek1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cq1', '72.cp1', '72.fb1', '72.fi1'], 'contains': ['288.bl1', '288.bn1', '288.bs1', '432.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1134693, 2951738, 37882213173], 'label': '3456.oc.144.ek1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.ek1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ek1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936560
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.el1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cr1', '72.o1', '72.bn1', '72.dm1', '72.do1', '72.fm1'], 'contains': ['288.u1', '288.bc1', '288.bu1', '288.cb1', '288.ch1', '432.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 1862886, 2588323, 38480884533], 'label': '3456.oc.144.el1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.el1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.el1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936561
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.em1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cs1', '72.z1', '72.bo1', '72.dn1', '72.dp1', '72.dq1', '72.dr1', '72.fm1'], 'contains': ['288.u1', '288.v1', '288.v2', '288.bu1', '288.cb1', '288.cc1', '432.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [13412085385, 1862886, 2588323, 38480884533], 'label': '3456.oc.144.em1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.em1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.em1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936562
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.en1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cr1', '72.m1', '72.bp1', '72.dm1', '72.dn1', '72.fn1'], 'contains': ['288.w1', '288.bd1', '288.bu1', '288.cd1', '288.ci1', '432.ci1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39799592563, 13412085767, 1862886, 2588323], 'label': '3456.oc.144.en1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.en1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.en1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936563
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.eo1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cs1', '72.n1', '72.bx1', '72.do1', '72.dp1', '72.dq1', '72.ds1', '72.fn1'], 'contains': ['288.w1', '288.x1', '288.x2', '288.bu1', '288.cd1', '288.ce1', '432.cj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [39799592563, 13412085385, 1862886, 2588323], 'label': '3456.oc.144.eo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.eo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936564
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.ep1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ct1', '72.cc1', '72.dm1', '72.dp1', '72.dt1', '72.fo1'], 'contains': ['288.y1', '288.be1', '288.bu1', '288.cf1', '288.cl1', '432.ck1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 2588323, 1967535360, 38480884533], 'label': '3456.oc.144.ep1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.ep1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ep1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936565
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.eq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.ct1', '72.du1', '72.fp1'], 'contains': ['288.z1', '288.bf1', '288.bv1', '288.cg1', '288.cm1', '432.ck1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1862886, 37882213173, 2588323, 1967535360], 'label': '3456.oc.144.eq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '144.eq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936566
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.er1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cu1', '72.m1', '72.bn1', '72.dq1', '72.dt1', '72.fs1'], 'contains': ['288.be1', '288.bk1', '288.bu1', '288.cj1', '288.cn1', '432.cl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1862886, 2588323, 38480884533], 'label': '3456.oc.144.er1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.er1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.er1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936567
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '576.8553', 'aut_weyl_index': 72, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.e1', '6.f1', '6.t1'], 'contains': ['24.dk2', '24.dn1', '24.dr1', '24.ds1', '24.dv1', '36.cj1', '36.ck1'], 'core': '96.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 526, 13415398178, 602744206], 'label': '3456.oc.12.bs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
-
id: 201936568
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.es1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.cu1', '72.du1', '72.ft1'], 'contains': ['288.bf1', '288.bl1', '288.bv1', '288.ck1', '288.co1', '432.cl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 1862886, 37882213173, 2588323], 'label': '3456.oc.144.es1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '144.es1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.es1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936569
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.et1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.cv1', '72.n1', '72.bo1', '72.dn1', '72.do1', '72.dv1', '72.fo1', '72.fs1'], 'contains': ['288.be1', '288.bg1', '288.bg2', '288.bu1', '288.cj1', '288.cl1', '432.cm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967535625, 1862886, 2588323, 38480884533], 'label': '3456.oc.144.et1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.et1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.et1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936570
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.eu1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cv1', '72.dw1', '72.fp1', '72.ft1'], 'contains': ['288.bf1', '288.bh1', '288.bh2', '288.bv1', '288.ck1', '288.cm1', '432.cm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967535625, 1862886, 37882213173, 2588323], 'label': '3456.oc.144.eu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '144.eu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.eu1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936571
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.ev1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cw1', '72.a1', '72.o1', '72.bp1', '72.dr1', '72.ds1', '72.dt1', '72.dv1'], 'contains': ['288.s1', '288.bu1', '288.cp1', '432.cn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 38480884412, 526, 1862886], 'label': '3456.oc.144.ev1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.ev1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ev1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936572
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.ew1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cw1', '72.du1', '72.dw1', '72.ge1'], 'contains': ['288.t1', '288.bv1', '288.cq1', '432.cn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37882213052, 2587950, 526, 1862886], 'label': '3456.oc.144.ew1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '144.ew1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ew1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936573
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.ex1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cx1', '72.z1', '72.bw1', '72.dx1', '72.ea1', '72.en1', '72.eo2', '72.fm1'], 'contains': ['288.a1', '288.u1', '288.v2', '288.bc1', '432.co1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085385, 38480884412, 2588323, 1863007], 'label': '3456.oc.144.ex1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.ex1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ex1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936574
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.ex2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cx2', '72.z1', '72.bw2', '72.dy1', '72.dz1', '72.eb1', '72.ec1', '72.ed1', '72.ee1', '72.en2', '72.eo1', '72.fm1'], 'contains': ['288.u1', '288.v1', '288.bc1', '288.bw1', '432.co2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 13412085385, 1863138, 2588323], 'label': '3456.oc.144.ex2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.ex2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ex2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936575
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.ey1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cx1', '72.y1', '72.bx1', '72.ef1', '72.eh1', '72.en1', '72.eo2', '72.fn1'], 'contains': ['288.a1', '288.w1', '288.x2', '288.bd1', '432.co1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39799592563, 13412085385, 2588323, 1863007], 'label': '3456.oc.144.ey1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.ey1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ey1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936576
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.ey2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.cx2', '72.y2', '72.bx1', '72.eg1', '72.ei1', '72.ej1', '72.ek1', '72.el1', '72.em1', '72.en2', '72.eo1', '72.fn1'], 'contains': ['288.w1', '288.x1', '288.bd1', '288.bw1', '432.co2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [39799592563, 13412085385, 1863138, 2588323], 'label': '3456.oc.144.ey2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.ey2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ey2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936577
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.ez1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cn1', '48.cy1', '48.cz1', '72.bb1', '72.ep1', '72.eq1'], 'contains': ['288.by1', '432.cp1', '576.k1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2586614, 1967901282, 2588323, 1863007], 'label': '3456.oc.144.ez1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '144.ez1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ez1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936578
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1152.136369', 'aut_weyl_index': 36, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.f1', '6.s1'], 'contains': ['24.dl1', '24.dm1', '24.dr1', '24.dt1', '24.du1', '36.cl1', '36.cm1'], 'core': '96.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1863259, 38482338042, 2587950, 1967536007, 2951738, 526, 602744206], 'label': '3456.oc.12.bt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936579
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.fa1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.b1', '48.cy1', '72.cd1', '72.en1', '72.er1', '72.ev1', '72.fo1'], 'contains': ['288.a1', '288.y1', '288.bg1', '432.cp1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884412, 2588323, 1863007, 1967535360], 'label': '3456.oc.144.fa1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '144.fa1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fa1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936580
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.fa2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.da1', '72.cd2', '72.en2', '72.et1', '72.ew1', '72.ex1', '72.ey1', '72.fo1'], 'contains': ['288.y1', '288.bg2', '288.bw1', '432.cp2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 1863138, 2588323, 1967535360], 'label': '3456.oc.144.fa2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fa2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fa2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936581
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.fb1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.b1', '48.cz1', '72.es1', '72.fp1'], 'contains': ['288.z1', '288.bh1', '288.bx1', '432.cp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37882213052, 2588323, 1863007, 1967535360], 'label': '3456.oc.144.fb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '144.fb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fb1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
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id: 201936582
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.fb2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.da1', '72.eu1', '72.ez1', '72.fp1'], 'contains': ['288.z1', '288.bh2', '288.bx2', '432.cp2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863138, 37882212769, 2588323, 1967535360], 'label': '3456.oc.144.fb2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.fb2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fb2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936583
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.fc1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '48.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.db1', '48.dd1', '72.p1', '72.bq1', '72.dx1', '72.ef1', '72.er1', '72.fa1', '72.fq1'], 'contains': ['288.a1', '288.ba1', '288.bo1', '432.cq1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38480884412, 2226652, 2588323, 1863007], 'label': '3456.oc.144.fc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.fc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fc1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936584
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.fd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.db1', '48.de1', '72.es1', '72.fb1', '72.fr1'], 'contains': ['288.bb1', '288.bs1', '288.bx1', '432.cq1'], 'core': '864.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882213052, 2226652, 2588323, 1863007], 'label': '3456.oc.144.fd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bn1', 'old_label': '144.fd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fd1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936585
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.fe1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '24.t1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dc1', '72.q1', '72.br1', '72.dy1', '72.eg1', '72.et1', '72.fc1', '72.fq1'], 'contains': ['288.ba1', '288.bw1', '432.cr1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38482338042, 2588202, 2226652, 1863007], 'label': '3456.oc.144.fe1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.fe1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fe1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936586
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.ff1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dc1', '72.eu1', '72.fd1', '72.fr1'], 'contains': ['288.bb1', '288.bx2', '432.cr1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [2588202, 37883666682, 2226652, 1863007], 'label': '3456.oc.144.ff1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '144.ff1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ff1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 201936587
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.fg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '96.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.b1', '48.dd1', '48.de1', '72.r1', '72.ep1'], 'contains': ['288.by1', '432.cq1', '576.p1'], 'core': '864.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1137421, 2226652, 2588323, 1863007], 'label': '3456.oc.144.fg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '144.fg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fg1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936588
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.fh1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.df1', '72.y1', '72.bw1', '72.eo2', '72.fa1', '72.ff1', '72.fo1', '72.fs1'], 'contains': ['288.a1', '288.be1', '288.bg2', '288.bk1', '432.cs1'], 'core': '288.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 38480884412, 2588323, 1863007], 'label': '3456.oc.144.fh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936589
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '6912.ed', 'aut_weyl_index': 6, 'centralizer': '1152.a1', 'complements': ['864.bn1', '864.bq1', '864.bg1', '864.e1', '864.bj1', '864.g1', '864.bp1', '864.bt1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.f1', '12.r1', '16.a1', '16.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1137421, 13412085385, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.4.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1', '12.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '3456.oc', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '1152.157864'}
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id: 201936590
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.k1', '6.p1', '6.r1'], 'contains': ['24.b1', '36.cn1', '36.co1', '48.cy1', '48.ee1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1967901282, 1862886, 647, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.12.bu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.bu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201936591
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.fh2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.df2', '72.y2', '72.bw2', '72.eo1', '72.fc1', '72.fe1', '72.fg1', '72.fh1', '72.fj1', '72.fk1', '72.fo1', '72.fs1'], 'contains': ['288.be1', '288.bg1', '288.bk1', '288.bw1', '432.cs2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38480884129, 1967536007, 1863138, 2588323], 'label': '3456.oc.144.fh2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fh2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fh2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936592
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.fi1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.df1', '72.fb1', '72.fp1', '72.ft1'], 'contains': ['288.bf1', '288.bh2', '288.bl1', '288.bx1', '432.cs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [37882213052, 1967536007, 2588323, 1863007], 'label': '3456.oc.144.fi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.fi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fi1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936593
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.fi2', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.df2', '72.fd1', '72.fi1', '72.fl1', '72.fp1', '72.ft1'], 'contains': ['288.bf1', '288.bh1', '288.bl1', '288.bx2', '432.cs2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1967536007, 1863138, 37882212769, 2588323], 'label': '3456.oc.144.fi2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.fi2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fi2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936594
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fj1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '144.k2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dg1', '48.dh1', '48.di1', '72.p1', '72.bs1', '72.dx1', '72.eh1', '72.ev1', '72.ff1', '72.fu1'], 'contains': ['288.a1', '288.bi1', '288.bp1', '432.ct1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 13413586612, 2588323, 1863007], 'label': '3456.oc.144.fj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.fj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fj1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936595
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 864, 'centralizer': '72.q1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dj1', '72.q1', '72.bt1', '72.dz1', '72.ei1', '72.ew1', '72.fe1', '72.fu1'], 'contains': ['288.bi1', '288.bw1', '432.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [13413586379, 38482338042, 2588202, 1863007], 'label': '3456.oc.144.fk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fk1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936596
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '144.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.di1', '48.dk1', '72.s1', '72.bq1', '72.ea1', '72.ef1', '72.ev1', '72.ff1', '72.fv1'], 'contains': ['288.a1', '288.bj1', '288.bq1', '432.ct1'], 'core': '288.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [39799592563, 13413586612, 2588323, 1863007], 'label': '3456.oc.144.fl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1', 'old_label': '144.fl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fl1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936597
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '144.fm1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '288.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.cu1', '48.dg1', '48.dk1', '72.r1', '72.t1', '72.eq1'], 'contains': ['288.by1', '432.ct1', '576.w1'], 'core': '864.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [1137300, 13413586612, 2588323, 1863007], 'label': '3456.oc.144.fm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1', 'old_label': '144.fm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936598
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '144.fn1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.cv1', '48.dh1', '48.dk1', '72.u1'], 'contains': ['288.bz1', '432.ct1', '576.x1'], 'core': '864.a1', 'coset_action_label': None, 'count': 144, 'diagramx': None, 'generators': [39798141540, 13413586612, 2588323, 1863007], 'label': '3456.oc.144.fn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.w1', 'old_label': '144.fn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fn1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936599
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '72.br1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dj1', '72.v1', '72.br1', '72.eb1', '72.ej1', '72.ew1', '72.fg1', '72.fv1'], 'contains': ['288.bj1', '288.bw1', '432.cu1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [13413586379, 2588202, 39798138933, 1863007], 'label': '3456.oc.144.fo1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.fo1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936600
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fp1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '432.j2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dl1', '48.dm1', '48.dn1', '72.s1', '72.bs1', '72.ea1', '72.eh1', '72.er1', '72.fa1', '72.fw1'], 'contains': ['288.a1', '288.bm1', '288.br1', '432.cv1'], 'core': '288.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38480884412, 1968991665, 2588323, 1863007], 'label': '3456.oc.144.fp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '144.fp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936601
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.q1'], 'contains': ['24.dy1', '36.cn1', '36.cp1', '48.cz1', '48.ef1'], 'core': '72.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37882213052, 1137421, 1967901282, 526, 647, 1862886, 2588323], 'label': '3456.oc.12.bv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1', 'old_label': '12.bv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201936602
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fq1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1728, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.dn1', '48.do1', '48.dp1', '72.es1', '72.fb1', '72.fx1'], 'contains': ['288.bn1', '288.bt1', '288.bx1', '432.cv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [37882213052, 1968991665, 2588323, 1863007], 'label': '3456.oc.144.fq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cc1', 'old_label': '144.fq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936603
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fr1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.cy1', '48.dl1', '48.do1', '72.t1', '72.ep1'], 'contains': ['288.by1', '432.cv1', '576.bc1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1137421, 1968991665, 2588323, 1863007], 'label': '3456.oc.144.fr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1', 'old_label': '144.fr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fr1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 201936604
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '144.fs1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.cz1', '48.dl1', '48.dm1', '48.dp1', '72.u1'], 'contains': ['288.bz1', '432.cv1', '576.bd1'], 'core': '864.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [38482336681, 1968991665, 2588323, 1863007], 'label': '3456.oc.144.fs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.u1', 'old_label': '144.fs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936605
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '144.ft1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.da1', '48.dm1', '48.do1', '48.dp1'], 'contains': ['288.ca1', '432.cv1', '576.be1'], 'core': '864.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [37883665321, 1968991665, 2588323, 1863007], 'label': '3456.oc.144.ft1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.ft1', 'old_label': '144.ft1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ft1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 201936606
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dq1', '72.v1', '72.bt1', '72.ec1', '72.ek1', '72.et1', '72.fh1', '72.fw1'], 'contains': ['288.bm1', '288.bw1', '432.cw1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 38480884412, 2588071, 1969714258], 'label': '3456.oc.144.fu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936607
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fv1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.183', 'aut_weyl_index': 288, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dq1', '72.eu1', '72.fi1', '72.fx1'], 'contains': ['288.bn1', '288.bx2', '432.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1863259, 37882213052, 2588071, 1969714258], 'label': '3456.oc.144.fv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.fv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
-
id: 201936608
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.fw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '24.z1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dr1', '72.w1', '72.bu1', '72.dz1', '72.ed1', '72.ej1', '72.el1', '72.ex1', '72.fh1', '72.fj1', '72.fq1', '72.fy1'], 'contains': ['288.bo1', '288.bw1', '432.cx1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38482338042, 2588202, 2951738, 1863007], 'label': '3456.oc.144.fw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.fw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fw1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936609
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fx1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '72.w1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ds1', '72.w1', '72.bv1', '72.dy1', '72.ed1', '72.ek1', '72.em1', '72.ey1', '72.fg1', '72.fk1', '72.fu1', '72.fz1'], 'contains': ['288.bp1', '288.bw1', '432.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [38482338042, 2588202, 1863007, 13415398178], 'label': '3456.oc.144.fx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fx1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936610
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '144.fy1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '72.bu1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ds1', '72.x1', '72.bu1', '72.ec1', '72.ee1', '72.eg1', '72.el1', '72.ey1', '72.fe1', '72.fk1', '72.fv1', '72.ga1'], 'contains': ['288.bq1', '288.bw1', '432.cy1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 39798138933, 1863007, 13415398178], 'label': '3456.oc.144.fy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.fy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fy1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936611
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.fz1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '216.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dt1', '72.x1', '72.bv1', '72.eb1', '72.ee1', '72.ei1', '72.em1', '72.ex1', '72.fc1', '72.fj1', '72.fw1', '72.gb1'], 'contains': ['288.br1', '288.bw1', '432.cz1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 38480884412, 2588071, 1968991665], 'label': '3456.oc.144.fz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '144.fz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.fz1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936612
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '384.20051', 'aut_weyl_index': 108, 'centralizer': '96.bf1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.g1', '6.s1'], 'contains': ['24.c1', '24.dq1', '24.du1', '36.cq1', '36.cr1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [2951738, 38480884412, 526, 647, 1862886, 2588323, 604203618], 'label': '3456.oc.12.bw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.bw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
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id: 201936613
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '144.ga1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '48.dr1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.dr1', '72.ez1', '72.fi1', '72.fl1', '72.fr1', '72.gc1'], 'contains': ['288.bs1', '288.bx2', '432.cx1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 2951738, 37883666682, 1863007], 'label': '3456.oc.144.ga1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '144.ga1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ga1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 201936614
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.gb1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.38', 'aut_weyl_index': 864, 'centralizer': '432.cx1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.dt1', '72.ez1', '72.fd1', '72.fl1', '72.fx1', '72.gd1'], 'contains': ['288.bt1', '288.bx2', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 37882213052, 2588071, 1968991665], 'label': '3456.oc.144.gb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1', 'old_label': '144.gb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
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id: 201936615
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.gc1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.du1', '72.a1', '72.z1', '72.bx1', '72.fm1', '72.fn1', '72.fo1', '72.fq1', '72.fs1', '72.fu1', '72.fv1', '72.fw1', '72.fy1', '72.fz1', '72.ga1', '72.gb1'], 'contains': ['288.a1', '288.s1', '288.bu1', '288.bw1', '432.da1'], 'core': '288.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [38480884129, 526, 1862886, 2588323], 'label': '3456.oc.144.gc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '144.gc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936616
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '144.gd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.du1', '72.fp1', '72.fr1', '72.ft1', '72.fx1', '72.gc1', '72.gd1', '72.ge1'], 'contains': ['288.t1', '288.bv1', '288.bx1', '288.bx2', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [526, 1862886, 37882212769, 2588323], 'label': '3456.oc.144.gd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1', 'old_label': '144.gd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936617
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.ge1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dv1', '72.e1', '72.by1', '72.ci1', '72.dm1', '72.dn1'], 'contains': ['288.cb1', '288.ci1', '288.cl1', '288.cv1', '288.dn1', '432.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 38481612726, 1862886, 1969352442], 'label': '3456.oc.144.ge1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.ge1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ge1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936618
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gf1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dx2', '72.m1', '72.by1', '72.ch1', '72.cj1', '72.dn1'], 'contains': ['288.cc1', '288.ci1', '288.cj1', '288.cv1', '288.cw1', '432.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 38481612726, 13414673443, 1862886], 'label': '3456.oc.144.gf1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gf1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gf1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936619
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gg1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dv1', '72.ba1', '72.bf1', '72.ci1', '72.dm1', '72.do1'], 'contains': ['288.cd1', '288.ch1', '288.cl1', '288.cz1', '288.dn1', '432.db1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 1969352442], 'label': '3456.oc.144.gg1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gg1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936620
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '144.gh1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dw1', '72.bz1', '72.ch1', '72.dm1', '72.dp1', '72.gh1'], 'contains': ['288.cb1', '288.cd1', '288.cf1', '288.cw1', '288.da1', '288.dc1', '288.dj1', '432.dc1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 38481612726, 1862886, 1967535360], 'label': '3456.oc.144.gh1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gh1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936621
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gi1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.dx1', '72.e1', '72.bf1', '72.ch1', '72.dn1', '72.do1', '72.dq1', '72.gi1'], 'contains': ['288.cb1', '288.cd1', '288.cj1', '288.cv1', '288.cz1', '288.de1', '288.do1', '432.dd2'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967536007, 38481612726, 13412085385, 1862886], 'label': '3456.oc.144.gi1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gi1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936622
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gj1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.dy1', '72.n1', '72.bg1', '72.ci1', '72.cj1', '72.dn1', '72.dp1', '72.gi1'], 'contains': ['288.cc1', '288.cd1', '288.cl1', '288.cv1', '288.dd1', '288.dd2', '432.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [38481612726, 13414673443, 1862886, 1969352442], 'label': '3456.oc.144.gj1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gj1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gj1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936623
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.q1'], 'contains': ['24.dy1', '36.b1', '36.cr1', '48.de1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37882213052, 1137421, 2951738, 526, 647, 1862886, 2588323], 'label': '3456.oc.12.bx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '12.bx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
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id: 201936624
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gk1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dz1', '72.m1', '72.bf1', '72.cj1', '72.dq1', '72.gh1'], 'contains': ['288.cc1', '288.cd1', '288.cn1', '288.cw1', '288.de1', '432.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 13414673191, 1969352190], 'label': '3456.oc.144.gk1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gk1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936625
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gl1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dx2', '72.ba1', '72.bn1', '72.ch1', '72.cm1', '72.do1'], 'contains': ['288.ce1', '288.ch1', '288.cj1', '288.cz1', '288.da1', '432.dd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [1967536007, 38481612726, 13414673070, 1862886], 'label': '3456.oc.144.gl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gl1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gl1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936626
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gm1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.dy1', '72.f1', '72.bo1', '72.ci1', '72.cm1', '72.do1', '72.dp1', '72.gi1'], 'contains': ['288.cb1', '288.ce1', '288.cl1', '288.cz1', '288.dd1', '288.dd2', '432.de1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [38481612726, 13412085385, 1862886, 1969352442], 'label': '3456.oc.144.gm1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gm1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gm1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936627
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gn1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.dz1', '72.e1', '72.bn1', '72.cm1', '72.dq1', '72.gh1'], 'contains': ['288.cb1', '288.ce1', '288.cn1', '288.da1', '288.de1', '432.df1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085646, 38481612726, 1862886, 1969352190], 'label': '3456.oc.144.gn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gn1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gn1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936628
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.go1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ea1', '72.cc1', '72.ch1', '72.cn1', '72.dp1', '72.gh1'], 'contains': ['288.cc1', '288.ce1', '288.cf1', '288.dc1', '288.de1', '432.dg1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [38481612726, 1862886, 13414673191, 1967535360], 'label': '3456.oc.144.go1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.go1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.go1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936629
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gp1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.eb1', '72.n1', '72.bo1', '72.cj1', '72.cm1', '72.cn1', '72.dq1', '72.gi1'], 'contains': ['288.cc1', '288.ce1', '288.cj1', '288.dd1', '288.dd2', '288.de1', '432.dh1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [1967536007, 38481612726, 1862886, 13414673322], 'label': '3456.oc.144.gp1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gp1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gp1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936630
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.gq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ec1', '72.ce1', '72.ch1', '72.dm1'], 'contains': ['288.cf1', '288.ch1', '288.ci1', '288.dj1', '288.do1', '432.di1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [38481612726, 13414673070, 1862886, 1967535360], 'label': '3456.oc.144.gq1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gq1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936631
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.gr1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.n1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ed1', '72.o1', '72.by1', '72.dr1', '72.gh1', '72.gi1'], 'contains': ['288.cb1', '288.cc1', '288.cp1', '432.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 38480883894, 13412085385, 1862886], 'label': '3456.oc.144.gr1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gr1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gr1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936632
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.gs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ed1', '72.ba1', '72.bp1', '72.ds1', '72.gh1', '72.gi1'], 'contains': ['288.cd1', '288.ce1', '288.cp1', '432.dj1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 13412085385, 39799592190, 1862886], 'label': '3456.oc.144.gs1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '144.gs1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936633
{'ambient': '3456.oc', 'aut_centralizer_order': 24, 'aut_label': '144.gt1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '864.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cn1', '48.ee1', '48.ef1', '72.bc1'], 'contains': ['288.cr1', '432.dk1', '576.k1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 72, 'diagramx': None, 'generators': [2587950, 1967901282, 1862886, 1137042], 'label': '3456.oc.144.gt1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.bc1', 'old_label': '144.gt1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gt1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 201936634
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.c1', '6.h1', '6.r1'], 'contains': ['24.b1', '36.cs1', '36.cu1', '48.dg1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1862886, 647, 13415398178, 38480884412, 2588323, 526, 1137421], 'label': '3456.oc.12.by1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.by1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201936635
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.gu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.ee1', '48.eg1', '72.ce1', '72.dt1', '72.gh1'], 'contains': ['288.cf1', '288.cn1', '288.cp1', '432.dk1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [2587950, 38480883894, 1862886, 1969352190], 'label': '3456.oc.144.gu1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1', 'old_label': '144.gu1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gu1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
-
id: 201936636
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '144.gv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.ef1', '48.eg1', '72.du1'], 'contains': ['288.cg1', '288.co1', '288.cq1', '432.dk1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37882212534, 2587950, 1862886, 1969352190], 'label': '3456.oc.144.gv1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bv1', 'old_label': '144.gv1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gv1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
-
id: 201936637
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '108.l1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.eh1', '72.ba1', '72.by1', '72.dt1', '72.dv1', '72.gi1'], 'contains': ['288.cj1', '288.cl1', '288.cp1', '432.dl1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [2587950, 1967536007, 38480883894, 1862886], 'label': '3456.oc.144.gw1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '144.gw1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gw1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936638
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.eh1', '72.du1', '72.dw1'], 'contains': ['288.ck1', '288.cm1', '288.cq1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [37882212534, 2587950, 1967536007, 1862886], 'label': '3456.oc.144.gx1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cp1', 'old_label': '144.gx1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gx1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936639
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '144.gy1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['48.ei1', '72.ca1', '72.dc1'], 'contains': ['288.cu1', '288.cx1', '288.cy1', '288.db1', '288.dc1', '288.dh1', '288.dk1', '432.dm1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 216, 'diagramx': None, 'generators': [38480520960, 2226652, 13413219813, 1967535360], 'label': '3456.oc.144.gy1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '144.gy1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gy1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936640
{'ambient': '3456.oc', 'aut_centralizer_order': 16, 'aut_label': '144.gz1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '216.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['48.ej1', '72.j1', '72.bk1', '72.dc1'], 'contains': ['288.cu1', '288.cx1', '288.cy1', '288.db1', '288.dd2', '288.dl1', '288.dp1', '432.dn1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 432, 'diagramx': None, 'generators': [1968627247, 38480520960, 2226652, 13414673322], 'label': '3456.oc.144.gz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bf1', 'old_label': '144.gz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.gz1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 201936641
{'ambient': '3456.oc', 'aut_centralizer_order': 1728, 'aut_label': '192.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '12.d1', 'complements': ['18.r1', '18.d1', '18.f1', '18.g1', '18.s1'], 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '96.a1', '96.e1', '96.f1', '96.g1', '96.h1', '96.j1', '96.m1'], 'contains': ['384.a1', '576.a1', '576.b1'], 'core': '192.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [602743680, 38480520960, 13412085120], 'label': '3456.oc.192.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1', 'normal_contained_in': ['48.a1', '96.a1'], 'normal_contains': ['384.a1', '576.a1'], 'normalizer': '1.a1', 'old_label': '192.a1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.227', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936642
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '192.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '36.b1', 'complements': ['18.d1', '18.f1', '18.g1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1', '96.a1', '96.r1', '96.bk1', '96.by1', '96.ce1', '96.cf1', '96.cg1'], 'contains': ['384.a1', '576.l1', '576.m1'], 'core': '192.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [602743680, 38480520960, 1967535360], 'label': '3456.oc.192.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1', 'normal_contained_in': ['48.b1', '96.a1'], 'normal_contains': ['384.a1'], 'normalizer': '1.a1', 'old_label': '192.b1', 'projective_image': '3456.oc', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.227', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936643
{'ambient': '3456.oc', 'aut_centralizer_order': 108, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '192.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.c1', '48.d1', '64.a1', '96.c1', '96.d1', '96.n1'], 'contains': ['384.b1', '576.b1', '576.c1', '576.d1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137421, 38480520960, 13412085120], 'label': '3456.oc.192.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '192.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936644
{'ambient': '3456.oc', 'aut_centralizer_order': 108, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '192.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.n1', '48.t1', '64.a1', '96.i1', '96.k1', '96.n1'], 'contains': ['384.b1', '576.a1', '576.c1'], 'core': '576.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1137421, 39797775360, 13412085120], 'label': '3456.oc.192.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '192.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936645
{'ambient': '3456.oc', 'aut_centralizer_order': 3, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1152.157852', 'aut_weyl_index': 36, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.i1'], 'contains': ['24.dx1', '36.cs1', '36.cv1', '48.dh1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1862886, 604926858, 647, 13415398178, 38480884412, 2588323, 526], 'label': '3456.oc.12.bz1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '12.bz1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1', 'subgroup_fusion': None, 'weyl_group': '192.1538'}
-
id: 201936646
{'ambient': '3456.oc', 'aut_centralizer_order': 54, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '384.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.o1', '48.u1', '64.a1', '96.l1'], 'contains': ['384.c1', '576.a1', '576.d1'], 'core': '576.a1', 'coset_action_label': None, 'count': 64, 'diagramx': None, 'generators': [604926858, 39797775360, 13412085120], 'label': '3456.oc.192.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1', 'old_label': '192.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936647
{'ambient': '3456.oc', 'aut_centralizer_order': 576, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '12.bw1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.b1', '96.e1', '96.o1', '96.p1', '96.q1', '96.q2', '96.r1', '96.s1', '96.t1', '96.u1', '96.v1', '96.v2', '96.w1', '96.x1', '96.y1', '96.z1', '96.ba1', '96.bb1', '96.bc1', '96.bf1'], 'contains': ['384.a1', '576.e1', '576.f1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1134693, 38480884533], 'label': '3456.oc.192.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '192.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936648
{'ambient': '3456.oc', 'aut_centralizer_order': 864, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1', '96.o1', '96.bc1', '96.bi1', '96.bj1', '96.bk1', '96.bl1', '96.bm1', '96.bn1', '96.bo1', '96.br1'], 'contains': ['384.a1', '576.g1', '576.h1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [38481612726, 1862886, 604203366], 'label': '3456.oc.192.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '192.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936649
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '36.cq1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['96.e1', '96.g1', '96.p1', '96.q1', '96.q2', '96.bi1', '96.bj1', '96.bu1', '96.bv1', '96.bw1', '96.bx1', '96.by1', '96.bz1', '96.bz2', '96.ca1'], 'contains': ['384.a1', '576.i1', '576.j1'], 'core': '384.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [602743680, 38480520960, 13413948127], 'label': '3456.oc.192.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '192.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936650
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '576.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.cy1', '48.ee1', '64.b1', '96.n1', '96.cb1', '96.cd1'], 'contains': ['384.b1', '576.k1', '576.l1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1967901282, 1137042, 38480520960], 'label': '3456.oc.192.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '192.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936651
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '1152.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.cz1', '48.ef1', '64.b1', '96.cc1'], 'contains': ['384.d1', '576.k1', '576.m1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [37881446400, 1967901282, 1137042], 'label': '3456.oc.192.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cc1', 'old_label': '192.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 201936652
{'ambient': '3456.oc', 'aut_centralizer_order': 432, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '48.dc1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1', '96.h1', '96.s1', '96.bu1', '96.ce1', '96.ch1'], 'contains': ['384.a1', '576.n1', '576.o1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 38480520960, 2226652], 'label': '3456.oc.192.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '192.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936653
{'ambient': '3456.oc', 'aut_centralizer_order': 108, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '192.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dd1', '64.c1', '96.c1', '96.i1', '96.cb1'], 'contains': ['384.b1', '576.n1', '576.p1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [1137042, 38480520960, 2226652], 'label': '3456.oc.192.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '192.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936654
{'ambient': '3456.oc', 'aut_centralizer_order': 108, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '384.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.de1', '64.c1', '96.cc1'], 'contains': ['384.d1', '576.o1', '576.p1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [37881446400, 1137042, 2226652], 'label': '3456.oc.192.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.f1', 'old_label': '192.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936655
{'ambient': '3456.oc', 'aut_centralizer_order': 288, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['96.f1', '96.j1', '96.p1', '96.t1', '96.bi1', '96.bl1', '96.bv1', '96.bw1', '96.cf1', '96.ci1', '96.cj1'], 'contains': ['384.a1', '576.q1', '576.r1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 13412085385, 38480520960], 'label': '3456.oc.192.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '192.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936656
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 72, 'centralizer': '288.bw1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '6.g1', '6.j1', '6.t1'], 'contains': ['24.c1', '24.ds1', '24.dv1', '36.cs1', '36.ct1'], 'core': '24.c1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1862886, 647, 13415398178, 38480884412, 2588323, 526, 604203618], 'label': '3456.oc.12.ca1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.ca1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1', 'subgroup_fusion': None, 'weyl_group': '96.230'}
-
id: 201936657
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '108.bo1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['96.g1', '96.r1', '96.u1', '96.v1', '96.v2', '96.bm1', '96.bn1', '96.bv1', '96.bz1', '96.bz2', '96.ch1', '96.ci1', '96.ck1'], 'contains': ['384.a1', '576.s1', '576.t1'], 'core': '384.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [602743680, 1968627499, 38480520960], 'label': '3456.oc.192.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '192.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936658
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '576.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dg1', '64.d1', '96.c1', '96.k1', '96.cd1'], 'contains': ['384.b1', '576.u1', '576.w1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [13414311772, 1137042, 38480520960], 'label': '3456.oc.192.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '192.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936659
{'ambient': '3456.oc', 'aut_centralizer_order': 18, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '1152.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dh1', '64.d1', '96.l1'], 'contains': ['384.c1', '576.u1', '576.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [604927321, 13414311772, 38480520960], 'label': '3456.oc.192.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.l1', 'old_label': '192.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936660
{'ambient': '3456.oc', 'aut_centralizer_order': 144, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '144.fe1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.d1', '96.h1', '96.m1', '96.w1', '96.bu1', '96.bx1', '96.cg1', '96.ck1'], 'contains': ['384.a1', '576.u1', '576.v1'], 'core': '384.a1', 'coset_action_label': None, 'count': 24, 'diagramx': None, 'generators': [602743680, 13414311772, 38480520960], 'label': '3456.oc.192.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '192.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 201936661
{'ambient': '3456.oc', 'aut_centralizer_order': 36, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '576.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dk1', '64.d1', '96.d1', '96.i1', '96.cd1'], 'contains': ['384.b1', '576.v1', '576.w1', '576.x1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 32, 'diagramx': None, 'generators': [39797775360, 13414311772, 1137042], 'label': '3456.oc.192.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.c1', 'old_label': '192.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936662
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1', '96.u1', '96.x1', '96.bk1', '96.bm1', '96.bo1', '96.bw1', '96.ca1', '96.cj1'], 'contains': ['384.a1', '576.y1', '576.z1'], 'core': '384.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [602743680, 1967536007, 38480520960], 'label': '3456.oc.192.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '192.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936663
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '192.u1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dl1', '64.e1', '96.d1', '96.k1', '96.cb1'], 'contains': ['384.b1', '576.ba1', '576.bc1', '576.bd1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [1137042, 38480520960, 1970078819], 'label': '3456.oc.192.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.x1', 'old_label': '192.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.u1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936664
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '192.v1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['48.dm1', '64.e1', '96.l1'], 'contains': ['384.c1', '576.ba1', '576.bd1', '576.be1'], 'core': '1152.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [604927215, 38480520960, 1970078819], 'label': '3456.oc.192.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.l1', 'old_label': '192.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.v1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936665
{'ambient': '3456.oc', 'aut_centralizer_order': 48, 'aut_label': '192.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '432.cr1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.e1', '96.m1', '96.y1', '96.bx1', '96.ce1', '96.ch1'], 'contains': ['384.a1', '576.ba1', '576.bb1'], 'core': '384.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [602743680, 38480520960, 1970078819], 'label': '3456.oc.192.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.w1', 'old_label': '192.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.w1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936666
{'ambient': '3456.oc', 'aut_centralizer_order': 12, 'aut_label': '192.x1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.do1', '64.e1', '96.cc1'], 'contains': ['384.d1', '576.bb1', '576.bc1', '576.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 96, 'diagramx': None, 'generators': [37881446400, 1137042, 1970078819], 'label': '3456.oc.192.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '96.cc1', 'old_label': '192.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.x1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
-
id: 201936667
{'ambient': '3456.oc', 'aut_centralizer_order': 2, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '1728.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.d1', '6.h1', '6.p1'], 'contains': ['24.b1', '36.cw1', '36.cy1', '36.cz1', '48.dl1'], 'core': '24.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1137421, 38480884412, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.12.cb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.cb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
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id: 201936668
{'ambient': '3456.oc', 'aut_centralizer_order': 6, 'aut_label': '192.y1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.dp1', '64.e1'], 'contains': ['384.e1', '576.bb1', '576.bd1', '576.be1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 192, 'diagramx': None, 'generators': [604927215, 37881446400, 1970078819], 'label': '3456.oc.192.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '192.y1', 'old_label': '192.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.y1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
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id: 201936669
{'ambient': '3456.oc', 'aut_centralizer_order': 1152, 'aut_label': '216.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '6.b1', 'complements': ['16.c1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.ge1', '72.gf1', '72.gg1', '108.l1', '108.bn1', '108.bo1', '108.bp1', '108.bq1'], 'contains': ['432.cn1', '432.da1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [526, 647, 1862886, 2588323], 'label': '3456.oc.216.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '72.b1'], 'normal_contains': ['864.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '3456.oc', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 201936670
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.c1', '72.bd1', '108.a1', '108.g1', '108.m1'], 'contains': ['432.a1', '432.b1', '432.e1', '432.v1', '432.y1', '432.bu1', '432.by1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [265, 13412085385, 1862886, 2226652], 'label': '3456.oc.216.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '216.b1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936671
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.d1', '72.be1', '108.a1', '108.h1', '108.m1'], 'contains': ['432.a1', '432.d1', '432.f1', '432.y1', '432.z1', '432.bz1', '432.ca1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [526, 1968991665, 1134054, 13413219692], 'label': '3456.oc.216.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.c1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936672
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.e1', '72.bf1', '108.b1', '108.k1', '108.n1'], 'contains': ['432.a1', '432.g1', '432.k1', '432.l1', '432.m1', '432.s1', '432.w1', '432.ba1', '432.db1', '432.dd2', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1967536007, 13412085385, 526, 1862886], 'label': '3456.oc.216.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.d1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201936673
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.f1', '72.bg1', '108.a1', '108.b1', '108.r1'], 'contains': ['432.a1', '432.h1', '432.h2', '432.l1', '432.t1', '432.x1', '432.be1', '432.be2', '432.de1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13412085646, 1969352563, 526, 1862886], 'label': '3456.oc.216.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.e1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936674
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.g1', '72.bh1', '108.c1', '108.d1', '108.m1'], 'contains': ['432.b1', '432.c1', '432.f1', '432.bu1', '432.bx1', '432.bz1', '432.cg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693, 2226652], 'label': '3456.oc.216.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.f1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936675
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.h1', '72.bi1', '108.c1', '108.e1', '108.m1'], 'contains': ['432.c1', '432.d1', '432.e1', '432.by1', '432.ca1', '432.cg1', '432.ch1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1967536007, 1134693, 2951738], 'label': '3456.oc.216.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.g1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936676
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.i1', '72.bj1', '108.a1', '108.d1', '108.o1'], 'contains': ['432.b1', '432.f1', '432.h1', '432.bd1', '432.bi1', '432.bw1', '432.cb1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13413948258, 1134693, 2226652, 1968627378], 'label': '3456.oc.216.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.h1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936677
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.j1', '72.bk1', '108.a1', '108.c1', '108.p1'], 'contains': ['432.b1', '432.d1', '432.h2', '432.o1', '432.bc1', '432.bg1', '432.bv1', '432.cc1', '432.dn1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627247, 1134693, 2226652, 13412085120], 'label': '3456.oc.216.i1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.i1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 201936678
{'ambient': '3456.oc', 'aut_centralizer_order': 1, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3456.di', 'aut_weyl_index': 12, 'centralizer': '3456.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.i1'], 'contains': ['24.dx1', '36.cw1', '36.cz1', '36.da1', '48.dm1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [604926858, 38480884412, 526, 647, 1862886, 1968991665, 2588323], 'label': '3456.oc.12.cc1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '12.cc1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1', 'subgroup_fusion': None, 'weyl_group': '576.8660'}
-
id: 201936679
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.k1', '72.bl1', '108.a1', '108.e1', '108.o1'], 'contains': ['432.d1', '432.e1', '432.h1', '432.bh1', '432.bj1', '432.cb1', '432.cd1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13413948258, 1134693, 2951738, 1968627378], 'label': '3456.oc.216.j1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.j1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936680
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.l1', '72.bm1', '108.a1', '108.c1', '108.q1'], 'contains': ['432.e1', '432.f1', '432.h2', '432.bk1', '432.bl1', '432.ce1', '432.cf1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968627247, 1134693, 2951738, 13412085120], 'label': '3456.oc.216.k1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.k1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936681
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.m1', '72.bn1', '108.k1', '108.n1'], 'contains': ['432.c1', '432.g1', '432.i1', '432.k1', '432.m1', '432.ba1', '432.bf1', '432.ci1', '432.cl1', '432.dd1', '432.df1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [13412085767, 1967536007, 1862886, 2588323], 'label': '3456.oc.216.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.l1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201936682
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.n1', '72.bo1', '108.b1', '108.k1', '108.r1'], 'contains': ['432.g1', '432.h1', '432.h2', '432.i1', '432.k1', '432.l1', '432.be3', '432.be4', '432.bm1', '432.bm2', '432.cj1', '432.cm1', '432.de1', '432.dh1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 648, 'diagramx': None, 'generators': [13412085385, 1967535625, 1862886, 2588323], 'label': '3456.oc.216.m1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.m1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201936683
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.o1', '72.bp1', '108.b1', '108.l1', '108.n1'], 'contains': ['432.a1', '432.i1', '432.n1', '432.s1', '432.ci1', '432.cn1', '432.dj1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [13412085646, 2587950, 526, 1862886], 'label': '3456.oc.216.n1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1', 'old_label': '216.n1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 201936684
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '72.cd2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.p1', '72.r1', '72.bq1', '108.c1', '108.g1', '108.o1'], 'contains': ['432.b1', '432.e1', '432.j1', '432.bd1', '432.bh1', '432.cq1', '432.ct1'], 'core': '864.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [2226652, 2588323, 1863007, 13413948127], 'label': '3456.oc.216.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1', 'old_label': '216.o1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936685
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '36.bf1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.q1', '72.br1', '108.d1', '108.g1', '108.p1'], 'contains': ['432.b1', '432.j2', '432.bc1', '432.cr1', '432.cu1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [2588202, 2226652, 1863007, 13413948127], 'label': '3456.oc.216.p1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.p1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936686
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '216.bb2', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.s1', '72.t1', '72.u1', '72.bs1', '108.c1', '108.h1', '108.o1'], 'contains': ['432.d1', '432.f1', '432.j1', '432.bi1', '432.bj1', '432.ct1', '432.cv1'], 'core': '864.a1', 'coset_action_label': None, 'count': 324, 'diagramx': None, 'generators': [1968991665, 2588323, 1863007, 13413948127], 'label': '3456.oc.216.q1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.q1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 201936687
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.12', 'aut_weyl_index': 1728, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.v1', '72.bt1', '108.e1', '108.h1', '108.p1'], 'contains': ['432.d1', '432.j2', '432.bg1', '432.cu1', '432.cw1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1863259, 2588071, 1969714258, 13413219692], 'label': '3456.oc.216.r1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.r1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936688
{'ambient': '3456.oc', 'aut_centralizer_order': 96, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '36.bg1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.w1', '72.bu1', '108.e1', '108.f1', '108.g1', '108.i1', '108.q1'], 'contains': ['432.e1', '432.j2', '432.bk1', '432.cx1', '432.cy1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [2588202, 2951738, 1863007, 13413948127], 'label': '3456.oc.216.s1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.s1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936689
{'ambient': '3456.oc', 'aut_centralizer_order': 4, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '3456.hx', 'aut_weyl_index': 12, 'centralizer': '864.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '6.j1', '6.s1'], 'contains': ['24.c1', '24.dt1', '24.dw1', '36.cw1', '36.cx1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [38480884412, 526, 647, 1862886, 1968991665, 2588323, 604203618], 'label': '3456.oc.12.cd1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.cd1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1', 'subgroup_fusion': None, 'weyl_group': '288.1040'}
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id: 201936690
{'ambient': '3456.oc', 'aut_centralizer_order': 32, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.x1', '72.bv1', '108.d1', '108.f1', '108.h1', '108.j1', '108.q1'], 'contains': ['432.f1', '432.j2', '432.bl1', '432.cy1', '432.cz1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1863259, 2588071, 1968991665, 13413219692], 'label': '3456.oc.216.t1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.t1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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id: 201936691
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.y1', '72.bw1', '108.c1', '108.k1', '108.r1'], 'contains': ['432.c1', '432.g1', '432.h2', '432.j1', '432.be1', '432.bm1', '432.bo1', '432.co1', '432.cs1'], 'core': '864.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [13413948258, 1967536007, 2588323, 1863007], 'label': '3456.oc.216.u1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.u1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936692
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.u2', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.y2', '72.bw2', '108.d1', '108.e1', '108.f1', '108.k1', '108.r1'], 'contains': ['432.c1', '432.g1', '432.h1', '432.j2', '432.be2', '432.bm2', '432.bo1', '432.co2', '432.cs2'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1967536007, 1863138, 2588323, 13413948127], 'label': '3456.oc.216.u2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.u2', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936693
{'ambient': '3456.oc', 'aut_centralizer_order': 192, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '18.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.z1', '72.bx1', '108.g1', '108.h1', '108.i1', '108.j1', '108.k1', '108.l1', '108.r1'], 'contains': ['432.a1', '432.i1', '432.j1', '432.j2', '432.t1', '432.cj1', '432.co1', '432.co2', '432.da1'], 'core': '864.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 2588323], 'label': '3456.oc.216.v1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '216.v1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936694
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.ba1', '72.by1', '108.b1', '108.n1'], 'contains': ['432.k1', '432.l1', '432.n1', '432.db1', '432.dd1', '432.dj1', '432.dl1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 108, 'diagramx': None, 'generators': [13412085767, 2587950, 1967536007, 1862886], 'label': '3456.oc.216.w1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.w1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201936695
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.bz1', '108.m1', '108.n1', '108.r1'], 'contains': ['432.a1', '432.c1', '432.k1', '432.p1', '432.q1', '432.u1', '432.bq1', '432.dc1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 81, 'diagramx': None, 'generators': [13412085646, 526, 1862886, 1967535360], 'label': '3456.oc.216.x1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '216.x1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936696
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.ca1', '108.m1', '108.o1', '108.p1'], 'contains': ['432.b1', '432.d1', '432.o1', '432.p1', '432.r1', '432.bp1', '432.br1', '432.dm1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2226652, 1967535360, 13412085120], 'label': '3456.oc.216.y1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.y1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936697
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '108.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.cb1', '108.m1', '108.o1', '108.q1'], 'contains': ['432.e1', '432.f1', '432.p1', '432.bs1', '432.bt1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1134693, 2951738, 1967535360, 13412085120], 'label': '3456.oc.216.z1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1', 'old_label': '216.z1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 201936698
{'ambient': '3456.oc', 'aut_centralizer_order': 64, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.cc1', '108.n1', '108.r1'], 'contains': ['432.g1', '432.i1', '432.l1', '432.p1', '432.q1', '432.bb1', '432.ck1', '432.dg1'], 'core': '3456.a1', 'coset_action_label': None, 'count': 162, 'diagramx': None, 'generators': [1862886, 2588323, 1967535360, 13412085120], 'label': '3456.oc.216.ba1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '216.ba1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 201936699
{'ambient': '3456.oc', 'aut_centralizer_order': 128, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.bb1', '72.cd1', '108.o1', '108.r1'], 'contains': ['432.h1', '432.j1', '432.p1', '432.bn1', '432.cp1'], 'core': '864.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [2588323, 1863007, 13413948127, 1967535360], 'label': '3456.oc.216.bb1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.bb1', 'projective_image': '3456.oc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
